It's not so much the amiga model as it is what Kickstart, CPU and Graphicchip it have. I reccon you look for compability for gaming and then it's no problem... both A1200 and A4000 although they have Kickstart3.x can be downgraded to 1.3 with software and degraders usually fix problems with graphic chips also. the Graphic chip you want is ofcause AGA as there's plenty of games only running on that and A1200 and A4000 is the only machines with this. Then there's the CPU... for the A1200 it's no problem... it comes with 020 and can be uppgrade to 030 for best speed for compability wise. For the A4000, though it does have it's 030 CPU cards, is probably not gonna cut it without at least a 040 or better CPU but that is quite bad on the compability front and you might wanna aim higher at a 060 CPU that's more compatible and realy speedy. The A4000 doesn't have a RF mod built in either so you can't hook it up to the TV as easily as the A1200.
My suggestion is: A1200, 030 CPU, 8MB Fastram (or more) and a 4GB HD for it. That'll be pleanty enough if it's hobby/gaming you're after... and it'll be nice to your wallet.