Hello,
Note that not all games will work on a 1200, even with WHDLoad or a "degrader" like TUDE (a degrader is a piece of software that emulates an older machine). I have no example in mind but I'm pretty sure of that, because WHDLoad does not support every game (but the most famous are supported), and a degrader isn't sufficient for numerous games.
Also there are games that will work, but not perfectly. For example, "Test Drive II" from Accolade has minor graphics problems on every machine that has not the original OCS graphic chipset (the 1200 has the AGA chipset), and no program has been able to solve this problem.
So in some cases, you may find that an older Amiga is useful : an A500, 1000 or 2000 with at least 1 Mb RAM, with the original Kickstart 1.3 (Kickstart is the Read Only Memory) and the original "OCS" graphics chipset.
But overall the A1200 is the best option for gaming, since it is common, compact, and it will let you play the more recent AGA games as well. But for playing the largest number of games, you will need a hard drive and 4 Mb of RAM.