While giving any kind of suggestion with your quite vague description is difficult, there are clear cut differences in how Magic (or more or less the vanilla concept of it) and cloce combat works.

Magic: Distance Attack, Range doesn't really matter. Effectivity mostly up to "Magic abilities" of the magician, little to no REAL skill involved (using magic might take practice, but in most vanilla themed fantasy universes, the only reallife skill involved really is the ability to concentrate the mind on using magic).

Thus stats that should affect magic is the "magic ability" of the magician (whatever you call it in YOUR universe) and his mental abilities (whatever mental techniques are used to focus magic)... if you leave the vanilla path, you could also have using magic involve a physical component (some kind of magic wand or whatever), reciting magical scrolls or whatever. To me, all this comes back to helping the magician concentrate on using his magic, so you could still collapse that all into 2 (or maybe only 1) stat.

Then there is the question of magical defense... what is the nature of magic in your universe, and what makes people resistant to it? Does it matter if they believe in magic? Do they need strong magical abilities themselves? Are there nullifier objects non-magicians can use to defend against magic?

Close Combat:

Close Combat, if we are talking about real world masters, is a very complex way of fighting involving many skills and physical abilities. Strength, Speed and stamina play a big role... but so does coordination or "fighting skill", expierience / tactical thinking, and last bu not least the equipment and fighting style.

While there are not really better or weaker styles, some styles and weapons struggle or overpower others. Which is why true masters often mastered more than one style, and good weapons often can be used in many different ways (most european two handed swords can be used with a spear like grip (for harnisch fechten for example, fighting against armoured opponents), a halberd is combining 3 weapons in one, and so on).

Of course, close combat is just that... while swords and axes can be thrown, that leaves the combatant without a weapon until he retrieves it, making it a last ditch choice... not to mention how inaccurate and short ranged such an action is.

Now, the balance between magician and meele fighters is up to you, but the way I see it is:

A Magicians power is mostly up to his magical skill. This ability can only be trained over long years of study, and that means he will be completly untrained in other ways of fighting. Equipment can help him augment his natural and trained abilites, but only to a certain degree.

A meele fighter has to rely on equipment and skill to similar degrees. While the "quality" of weapons, before we get into weird magical gear, is mostly on par (different steel might make a difference when sword clashes (and one of the blades break), but in all other cases, an inferior blade will cut through flesh just as well), the different weapon types will not only decide how the combantant has to fight, it will also take some skill and training to use a weapon type to full extent. Instead of just augmenting natural abilities, the equipment will make the difference here, then followed by the the amount of training and expierience the user has with that weapon type. Physical abilities will in the end tip the balance, but a weaker opponent can overcome a stronger one trhough skill and tactical thinking, thats why I rate that higher.

In the end, magiacian fighting a meele fighter will have the upper hand until the meele fighter can close the distance. Depending on his type of magic, and how strong you make your magic, he will be able to defend itself to varying degrees in close combat, but I personally wouldn't give the magician much chance in close combat.

Meele is a very quick and intense affair. The only reason why meele fighters can make the right decisions in spilt seconds is muscle memory and expierience. They not longer think how to parry and attack, they just do it... letting their mind be occupied with other things like higher tactical decisions, or keeping track of their surroundings while their arms move "on their own".

Now, a magician most probably has to "think" to use his magical abilities. Some of it might also be subconcious reactions, but in the end it is mostly the mind who is occupied. That means while using magic, they will loose track of their surrounding, they might not be able to make sound tactical judgements, and also, if they can use magic in the quick rythms of sword or axe blows, might be questionable.

Even if a magician can hold his own against a meele fighter in close combat, he will most probably be completly occupied with his defense, might be tricked by the meele fighter that can make more decisions while fighting as his mind is less occupied with offense and defense, and in the end the meele fighter is using more of his body while fighting, thus exhausting his body at a more distributed rate, while the magician will singularly use mental concetration and quickly grow tired.

TL;DR: If the meele fighter cannot get into meele range quickly, he will certainly loose. If he does, the magician might be able to use some magic tricks to defend the first few blows, but he will get killed quickly.

The only way for the magician to survive is to keep his distances and kill the meele fighter before he exhausts his mental abilities. The only way for the meele fighter to survive is to quickly close the distance and occupy the magician with his own attacks, before he can pull any magic that either is damaging enough to finish off the meele fighter, or harms his abilities to close the distance (stun or freeze magic, attacking the meele fighters legs).

If we want to transfer that to a simple system, give magic spells a minimal distance. Give the meele figther the ability to evade magic to some extent to prevent lame magical camping or tricks. Or some objects that nullify the magic. Give the magician abilities to defend himself in close combat, but only for a very short while or with the probability to fail... and with no option on offense. Give him ways to get away from the melee fighter.

The difference between a wizard and a warrior is that if you want to throw fireballs you need to keep enemies at a distance, while if you want to hack people with an axe you need to close in for melee combat.

No no no. See, this is what I was talking about. Wizard, warrior, fireballs etc. are just flavor to dress the system with. The difference between the classes has nothing to do with “warriors are like this, and wizards are like that.”

The very simple playing styles you've just presented are these:

(1) fights enemies from a distance,

(2) fights enemies from close-up.

You can now dress these styles in any way you like. So for (1) you can have:

(a) a Warrior throwing throwing axes,

(b) an Amazon throwing javelins,

( c) a Corsair shooting a pistol,

(d) a Ranger shooting a bow,

(e) a Marksman shooting a crossbow,

(f) a Thief throwing daggers,

(g) a Geomancer commanding the elements,

(h) a Wizard throwing fireballs,

and so on.

As you can see, you can dress your styles in any way you want. Want a cat shooting lasers from her eyes? Sure, go ahead.

The parameter that you mentioned, attack range, is just one out of many to differentiate styles. So let's make a quick list of simple parameters we could use.

1. Attack range:

(a) short,

(b) far,

( c) hybrid,

and anything inbetween.

2. Attack strength:

(a) high,

(b) mid,

( c) low,

(d) no attack.

3. Attack speed:

(a) slow,

(b) mid,

( c) fast.

4. Attack type:

(a) Type 1,

(b) Type 2,

( c) Type 3,

(d) Type 4,

...... (dress the styles later with names like physical, piercing, or whatever seems fitting).

5. Lifepoints:

(a) high,

(b) mid,

( c) low.

6. Attack resource:

(a) requires no resource to attack,

(b) requires a resource to attack.

7. Attack resource type:

(a) no resource,

(b) resource refills at events (e.g., rest),

( c) resource refills when using an item (e.g., a mana potion),

(d) resource must be found/bought/crafted (e.g., arrows).

So now from these we can create a huge variety of different styles. The more parameters we add, the more complex our styles become. Once we start giving a style different parameters depending on technique, it becomes even more complex (e.g., different spells having different attack speed and type).

Now let's create a random class from this for presentation purposes. Let's go with acacabc, that seems random enough. So we get:

Random Class

Attack range: short

Attack strength: low

Attack speed: slow

Attack type: Type 3

Lifepoints: high

Attack resource: requires a resource to attack

Attack resource type: resource refills when using an item

Alright, so short attack range and high lifepoints. Being a MMORPG veteran, this instantly reminds me of Tank classes, so it'll be a defender. Our class requires a resource to attack that refills when using an item, so we could make this resource Mana and the item Mana Potions, but that seems a little boring to me, so we'll spice it up. The resource is blood, and blood potions must be acquired from dead enemies. Attacking drains our heroic defender of his life energy, and he must refill it with blood drained from enemies. Sounds nice enough. His attack speed is slow, surely he must be using a heavy hammer. A hammer is blunt, so our Type 3 shall become blunt. His attack strength isn't high, but that's alright because his job is surely to defend his allies while he leaves the killing to them. Now to finish up, we just need a name and we have a class.

Vampire Knight/Blood Knight

Attack range: short

Attack strength: low

Attack speed: slow

Attack type: blunt

Lifepoints: high

Attack resource: blood

Attack resource type: use blood potions to refill blood (acquired from dead enemies)

You can surely go about it the other way, and start with a class name and go from there in any way that seems cool, but the playability ultimately lies in the system you create, not in what you name the classes or techniques. A warrior that throws fireballs? Sure, why not.

Is range a factor inside this game?

I like this question, because it underlines how vague the OP truly.

Many games get away with the range dimension to differentiate attacks, but they end up with a different problem (how is a bow any different from a magic missile) and must deal with this.

Rather, here, I would allow for range not to play an active part in game design and question how magic should differ from physical damage.

Since I generally consider magic to play a support role in most games (this may be highly inaccurate, so disregard as you please) I would diminish the sheer amount of damage but graft a special ability such as slowing down the enemy's attack, etc.

Therefore, the end-result is that a mage swarm vs a knight swarm would end in victory for the knights, but a mage behind a few knights could really start to give them the upper hand.

Without no additional knowledge on your game specifics that is all the advice I can provide.

Is range a factor inside this game?

I like this question, because it underlines how vague the OP truly.

Many games get away with the range dimension to differentiate attacks, but they end up with a different problem (how is a bow any different from a magic missile) and must deal with this.

It may be a different problem, but it's a solved problem - but to see the solution requires viewing attacks as more than just blobs of damage. Specifically, the different types of attack use different mechanics.

Just look at D&D, where the term "magic missile" comes from in the first place:

Magic missile automatically hits. Bows require a successful hit roll.

Magic missile can only be used a small, fixed number of times per game day. Bow use is limited only by the character's ammunition.

Magic missile requires the character be able to move and speak. Using a bow only requires them to be able to move.

Bow attacks can critically hit, magic missiles cannot.

So magic missiles have less variability (i.e. are more consistent), but also lower availability (i.e. there are more situations in which they are not usable) compared to bows. Both attacks have reasons why you would use it over the alternative - reasons that are missed when one just sees "oh, both attacks do an average of 3.5 damage per projectile", reasons that wouldn't exist if that 3.5 damage was all the designers thought about.

I'd take a step back and ask "why do I want different classes?" In a super simple rpg, flavor (or just having one class) might be enough, but there's all sorts of reasons classes can be good design. Complexity - Warrior=simple, Wizard=complex lets different styles of players enjoy what they enjoy most. A common design is to give the wizard low hp but many spells to choose from. The warrior will only have a couple choices at any given time (hit? health potion? flee?) but enough hp to survive mistakes. The wizard almost always has the right tool available, but if they reach for the wrong spell they don't have the hp to survive. The well played wizard > the warrior > the poorly played wizard. Gameplay - Sometimes each class just plays fundamentally different, where the warrior requires pressing the right button at the right time and the wizard requires strategic allocation of resources. It gives players a reason to replay, or have multiple classes in a party, or to choose the subgame they like better. Parties - With parties, choosing the right mix of classes can be a big part of the game. The classes don't need to be balanced against each other, they can each serve a different niche. If the niches overlap, you have interesting tradeoffs to make (two paladins, or a cleric and a knight?) Variety - If each class has a different distribution of skills, the optimal tactics by and against each class will vary. This is especially valuable in PVP, because each opponent requires you to shift your approach. A class who can occasionally use a high power attack might require constant maintenance of hp, while a more grinding class you can switch between extended attacks and extended or powerful healing. If classes can be developed in different ways, the battle also becomes one of information gathering. Chance - Some players are gamblers, some want to win every time. A common tradeoff is to give one way of playing that's more risky (usually the warrior) and another way (say, a rogue carefully drawing off individual enemies and killing them) that's much more certain to succeed but takes longer. Narrative - Sitting in a library carefully picking your spells from a weighty tome and wandering the armory choosing the perfect enchanted sword could have identical in game effects, but they feel different. Yeah, if it's "you shoot magic for 20 damage" or "you swing your axe for 20 damage" that's bad design, but if you play up the unique flavor of each class wherever you can, purely cosmetic differences can go a long way. How do you gain skills? Improve them? Can each class have its own special quests? It varies by every game. If yours has interesting choices and flavor, you should be able to find some way of varying the choices and flavor between classes.