This article on eHow lists some PS2 emulator requirements and they seem pretty low. Building your own computer will give you a lot more control and much better performance for the price. For between 50 and 80 dollars you can get a pretty decent CPU + GPU combo like this one. Then you want to find a motherboard that goes with the chip like this one (check the sockets to ensure they are compatible) and a cheap case that comes with a power supply and maybe looks snazzy like this. Buy a few gigs of ram ($25) (you shouldn't need more than 4) and a harddrive of your choice ($25-50)and assemble. In total this will cost maybe $200-300. Be fore-warned, I'm spec'ing this thing for one purpose, be as cheap as possible while still being functional. Now the real kicker is the OS, there are plenty of user friendly linux distros like ubuntu which won't cost you anything, but a legit copy of windows will run you $170 by itself (unless you're a student, then its cheaper).
Also for comparison against building one yourself: this is about what I spec'ed for you and that is with it on sale for $200 off!