This link (
Play Original Xbox Games on Xbox 360) has a list of original Xbox games you can (supposedly) play on the 360. To be honest, I don't know why anyone would want to play original Xbox games these days, because they'll look awful. Also, I did try to play Fable: The Lost Chapters on my 360 and it played
so badly. It had horrendous frame rate issues and was essentially unplayable. I don't know how well some of the others on the list would play, but there are some which have been remastered and re-released, so they'd probably be better. Now that the Xbox One exists though, you'll find that original Xbox games are remastered for that instead of the 360 (Voodoo Vince was an original Xbox game, and the remaster came out a few weeks ago for Xbox One.)
Minecraft is FANTASTIC! If you were to get an Xbox One, there are more and more Xbox 360 games that are backwards compatible on top of the Xbox One games that have already come out. If you were to get an Xbox 360, there are still loads of games that came out on it and also downloadable games too (better selection than the Xbox One has currently.)
EDIT: Forgot to add the link