Building a pc is easy, I used to work for Gateway a looong time ago building computers for them (yeah yeah, don't go dissing me now, it was the only decent job in the area before I moved).
It depends on what games you want to play as to how much horsepower you need.
I ran most of the games on my Pentium 450 and they worked fine. You could probably buy a used PC from somebody for cheap too if you watch the ads in the paper etc..
Otherwise, Here are some idea's to get you started.
Found this stuff on Newegg.com
MOTHERBOARD:
ECS "K7VTA3 V6.0" VIA KT333 Chipset Motherboard for AMD Socket A CPU -RETAIL
Model# K7VTA3 V6.0
Item # N82E16813135160 Cost is $33 Has an AGP slot, 6 USB ports and supports up to 2 Gigs of ram which is more than you would need.
You could save even more by getting this board:
Model#: M811LU
Item#: N82E16813185010 which is similar for only $25.
PROCESSOR:
You can get a 500 MHZ AMD for $15 OEM but you might want a little better. You can opt for the Model: AMD Athlon 1.33GHz for $48. This should be Excellent for what you want.
Then just toss in 512 Ram, your hard drive which you already have, your AGP video card, cheap cd-rom drive and floppy drive if you want.
When putting the machine together, it is best to do it on tile or wood floor (anything but carpet) to prevent building up ESD (electro static discharge). It's also a good idea to keep at least some part of your body (use your imagination here

) touching part of the unpainted metal case which will discharge any static like a grounding strap. If you have any questions, let us know.
Good luck