If you're not running 3d stuff or CHDs, you can use almost any PC really unless we're talking ancient. I had a 1.4 GHZ Pentium and all 2d stuff ran fine on MAME 0.85 for me - except for some of the Midway games like MK, MK2, MK3, UMK3, NBA Jam, and Rampage: World Tour. For those games I used Fastmame 0.71 and they ran fine.
I could even get KI and KI2 running full speed if I used the U64 emu.
The caveat of course is that emulation will not be as accurate using older versions of MAME or alternate emulators. That may or may not bother you.
It really depends on what games you want to play - if you're set on playing the aforementioned Midway games, you probably shouldn't go with something really weak. If all you want to play is classics, almost anything will work.
I had an old crappy Celeron 500 Mhz with 64 MB of ram and I had games running full speed using MAME 0.56. I even had MK3 running full speed with the sound disabled, so a little bit better machine probably could have run it full speed with sound on that MAME version.
If you could give us an idea of specs of the PCs that you're looking at, I'm sure there are people here who could tell you what will run and what won't on it.
