I does not matter what you give to the player. Tons of ammunition and weaponry - kill them by bacterias. A lot of medicaments - kill by radition. Anti rad gear - kill by a landfall. And so on, so on
You definitely should try being a Game Master in an pen & paper RPG, it extends the imagination of means to kill extrmelly well equipped and skilled player characters
Yep. And just plain bad luck can do a number on them as well. A friend once rolled a 1 in a d20 system ten times in a row. (And yes, he switched dice for most of them assuming someone swapped his for a trick die.)
What gear you start with depends on what environment you are dropping them in, what amount of challenge you want to give them, and what kind of a crafting system you want to offer.
Generally they will want a blade of some sort, a day or so of food, and something to hold a limited amount of water. Larger items like an axe would often be useful. Something to create fire, extra clothing/shelter elements, etc.
Also, you could go with something like a points based system where the player chooses what they take. Starting difficulty levels could then scale the prices for different things.