It seems a really big leap to me, you start liking games and from there you decide to be a 3D modeler just to create a game of your own.
Do you realize that games are produced by people that don´t need to know how to model ?, it´s just a bussiness for bussiness people, to create a good game there is needed alot more people than to create a good movie.
But the real problem I see is that modeling in 3D it´s just a kind of drawing, first of all you need to learn how to draw, then how to draw in 3D, and finally, be confident enough to create your 3D assets, wich can range from a bottle to a trailer truck, and some characters. You´ll need a lot of time to learn it all.
As others have said, there are open source programs that allow you to do all the needed tasks, even Blender has a game engine, tools aren´t a problem today.
Best regards