Im a student studying all aspects of games design so i can easely help you wiht this.

3ds max and maya are modeling programs there indistry standerd for creating 3d models for games they can be used as game engens of your a skilled programer but most developers just use a set engen (with rare exceptions sutch as the prince of persa seires and assasins creed whitch were made within 3ds max)

I would avoid both game maker as its not indistry standerd and dark basic as its far outdated, microsoft now have releced XNA if you truly want to get in to the indistry as a programer you would be best to learn XNA, C++ and direct x.

for a better understanding look up game mods, unless you plan to create an entirely new engen most games use a preset one and alter it to sute there needs.

Unreal 2004 (recently outdated with the unreal 3 engen) (UT, Gears of war, Bioshock ect)
Source engen (half life 2 and counter strike)
IDs engen (Quake)
Cry engen (recently outdated with the Cry 2 engen) (Far cry and crysis)

to get accses to the engen simply buy a game that uses it and the engen will come with it.

look on moddb for more infomation