@optician - Short answer for your question, of the 3 pieces of software you mentioned, you will do best with Unity 3D. You don't want to dive heavily into C/C++ so that rules out id Tech 3 (it's also a bit dated). Unity works with Javascript, C#, or Boo scripts attached to game objects and components so you can do as little or as much code as you feel comfortable with. Unreal is okay as well but I find the learning curve with Unity to be much shallower. You will put out a finished game more quickly and I think that is your ultimate goal, to make games.
@Andreas - I am currently using Unity 3D v2.6 to learn the engine for a personal project. I don't want to say it is impossible to make a AAA title with it but at the very least it is very unlikely.
For a prototype, all I did was import a moderately detailed model of a large space cruiser and Unity choked on it (meshes must not exceed 65,000 vertices). Granted that's an extreme example and it's fairly easy to use lower detail models but that's not the only issue. Being a space concept, I used accurate astronomical scale distances in a test using 1 Astronomical Unit between a planet and its star. Only to run into 32-bit signed floating point precision errors that caused the camera to jitter, stutter, and gyrate like a crack addict despite the values being several orders of magnitude below the 32-bit limit. I could set the far viewing plane to a maximum 1e+15 units at 60 degrees viewing angle before the camera started to go wonky.
Don't get me wrong, I like the engine and am a big fan. But for the purposes of AAA game development involving large teams with multi-million dollar budgets the currently available (to beginners) version of Unity is not as robust as Unreal Engine 3.5.
... id Tech 3 is a good place for a beginner to get a look at the C++ source code of a AAA quality game by the standards of several years ago but again, unless you want to go out and use someone else's tools written several years ago you will be spending a lot of your time constructing tools for the rest of your team before you can even start producing a "AAA" quality game.
Note: I am not saying you can't make a good game or even a great game. But it will not be competitive commercially with Modern Warfare 2, Halo 3, Gears of War 2, etc. That market is unforgiving with a different set of expectations and will not accept pre-DirectX 9 graphics quality.