Yeah, finding a system can be tough. I have three Amiga's, though I'm quite lucky to have them. The Amiga 1200 is a good option here because the accelerators for that model are actually relatively easy to find on eBay... usually for around $120 or so (Believe me, if it was that cheap and easy to install an accelerator in my Amiga 3000, I'd jump at the chance!). Just about every 1200 accelerator also has regular SIMM slots on it for memory, which is very helpful since that damn ZIP RAM is next to impossible to find.
With a 1200, a lower-end accelerator (say, a 68030), a modest hard drive and some extra RAM, you'll have a pretty powerful Amiga capable of running just about every Amiga game via WHDLoad... getting an Amiga 500 to that point would take a much larger amount of work and money.