I have an idea of an First-person RPG.

It's supposed to be a fantasy-based RPG, with the selection of multiple characters (at the same time), with very basic, old-fashioned graphics. Dialogue, stats, and inventory, items like armor, gauntlets, boots etc. Imagine Might & Magic-series if you can.

- Which engine would be the best to approach this task?

- Where is the best place to search for tutorials, and learning the basics?

I have understood that C# is a very usefull programming-language to know, but I am unsure of which engine would be the best for this kind of thing.

if you still want to go with an engine after the very good recommendation of doing a mod:

Unity 5 and Unreal Engine 4 are both good options, if you can stomach the learning curve.

Neither of both is as easy and accessible for a total beginner as a simpler 2D engine due to the complications of 3D Graphics and writing code for 3 dimensions.... but both are quite feature complete and have large communities and good tutorials to help you out if you get stuck.

Personally, I'd say Unity wins when it comes to user friendliness and accessibility (tutorials and API seemed better structured to me, many things that need to be done externaly in Unreal are integrated into the Unity editor, and you get the biggest asset store full of useful additions, many of which are free), while Unreal seem to win on renderer quality and performance (not by THAT much on renderer quality, but you have to work less hard to make things look good (if that matters to you), and it seems to still have the edge on performance IMO).

There is the Blueprint System and Material Editor in Unreal Engine 4 which allows you to drag and drop together runnable code in a node-based editor, so you can "program" without knowing C++ syntax (though I would urge you to learn at least the basics of programming before drag-and-dropping together your scripts).

Besides that, you need to learn C++ to get thing moving in Unreal Engine 4, which until now looks like more work to me than the C# scripting that is available in Unity thanks to Mono.

Also, people will tell you C++ is much harder to learn. Pointer magic n' Stuff. But let me assure you, if you are bright enough to learn C#, you will be able to learn C++. At least the bit that is needed to get your stuff moving in Unreal Engine 4 through C++ Code.

Now, you are talking about "oldfashioned Graphics"... are we talking about 2D or 3D Graphics? Because there is a lot of overhead that comes with 3D that could be avoided in 2D.

Especially if "oldfashioned Graphics" and "First person" mean early "3D-ish" RPGs like what was available in the 80's... most of them where still using 2D graphics to achieve an at the time spectacular 3D effect.

In this case, you could go with simpler Game Engines... maybe Game Maker.

I have an idea of an First-person RPG.

It's supposed to be a fantasy-based RPG, with the selection of multiple characters (at the same time), with very basic, old-fashioned graphics. Dialogue, stats, and inventory, items like armor, gauntlets, boots etc. Imagine Might & Magic-series if you can.

- Which engine would be the best to approach this task?

- Where is the best place to search for tutorials, and learning the basics?

I have understood that C# is a very usefull programming-language to know, but I am unsure of which engine would be the best for this kind of thing.

First Person, old fashioned graphics, and also an RPG?

I am guessing most people are thinking of something like Skyrim. If that is the case, then don't take this the wrong way. But if you ever find yourself asking that question, and list a complicated series of specification for the game, then you are better off dialing way back and taking Hodg's advice.

I think that you are talking about something along the lines of Eye of the Beholder, and Grimrock. If so... try Game Maker, or Unreal. Unreal and Unity are a bit complicated for this type of project. But Unreal can make things easier for you.