I have most of the major Amiga models: A500, A1200, A2000, A3000, A4000 (hate the A600 and didn't bother with the console CDTV and CD32).
For just gaming an A500 + external floppy drive or A1200 are probably the best. A1200's have the cheapest CPU upgrades and laptop IDE drives are easy to find for them. A500 are best for floppy booter games, gets pricey to buy a HD for the 500.
For the box Amigas I think the A3000 is the best built, still has SCSI, and has a built in flicker fixer/scan doubler so you can use any old VGA monitor. CPU upgrades for the 3000 are kind of pricey and so is memory (SIPP CHIPS). If you like this model make sure it comes with all the RAM you need, replace the CMOS battery before it kills anything (also HD info is stored by this battery so if it is dead the HD will not boot).
A4000 is the last Amiga made and the only boxed Amiga with AGA. It uses cheap (but slow) IDE drives and commodity 4MB 72 pin SIMMs.
A2000 is a good alternative for the A500 if you need a WB 1.3 machine that can take a HD (but 2091 controllers are getting expensive and so is the chip RAM they use which is needed for DMA transfers). While the machine is fairly large it only has spots for 2 3.5" floppies and one external 5.25" (used with PC cards or you can mount a HD or CDROM), not much space for a HD which is usually mounted on the SCSI controller(hardcard). Major issues with the CMOS battery leaking and killing the CPU socket, kind of bulky too.
The major issues with all of them (except the A3000) is you need to find either a working Amiga monitor with the correct cable or a very old VGA monitor that syncs to 15khz (early 1990's vintage, most are dead and trashed by now). You can buy a Zorro video card to use a VGA monitor with, but they are expensive and will not help if you want to play games (unless it does flicker fixing and scan doubling).
Also Amigas need specific keyboards (box machines) and mice which are kind of worn out and hard to find. You can usde most Atari 9 pin type joysticks for games.