If you're really set on a true FPS, I'd recommend using a pre-made engine that was specifically designed for it. The Quake and Doom code has all been released by id to open source specs and there are quite a few projects that take advantage of them. Other 3D engines like Crystal Space and Ogre 3D, as well as perhaps Blender Game Engine, would be other good places to start if you really want to create the FPS portion of the game from scratch.
Modding games is by far a superior entry-level experience in creating FPS-type games. If you don't have it already, I'd suggest Half-Life 2 or some other Source engine game (which can be gotten inexpensively, perhaps even free now) and look into the modding scene where there's a lot of established work and tutorials to learn from.