You might want to post your system specs - saying that it's a "Dell Optiplex GX1" isn't saying much - what the hell is that? Most people aren't going to go search Dell's site to find out what kind of computer you have. I, however, did...
And it's hard to find any info on Dell's site, but it looks like it's a Pentium II or Pentium III (depending on exact model). If so, then you're lucky to get Compiz running at all - in fact, just getting a relatively "heavy" distro like Mint running smoothly is a bit of a feat. If you want to run on a system that old, then definitely disable all visual effects, and hope for the best.
If you want a "cheap hardware solution", this is the best I can do: http://www.ascendtech.us/customkititems.asp?kc=DTA646000512160
Or go to pricewatch.com and check it out yourself. The one above looks like the best deal right now - $200 for a dual-core system is pretty good, although you might want some upgrades. If you go absolutely barebones, you can probably find a modern system for just over $100.