Building one is a good way to go. Difficulty level is about the same as stripping an AR-15 down including the bolt assembly. Pricing might be something like this...
Case w/400w power supply - $30
motherboard/CPU combo - $90 (say an AMD 3000)
memory - $90 (1GB)
optical drive - $40 (DVD-RW)
hard drive - $40 (120GB)
video card - $140 (GeForce 6600GT)
monitor - $100 (19" CRT)
keyboard/mouse - $15
Windows XP Home - $90
That's $620 and it'll play any game out there at a very good quality. The prices are either straight off PriceWatch.com, or a current/recent deal that isn't some weird/freaky price-matching thing, but may have a simple rebate. For example, people are getting 120GB hard drives for $20 after a pricematch/rebate, but just the rebate is about $40. If you already have a monitor, there's some savings. The case isn't anything fancy and may need an extra $5 for an extra fan.
A difficult part is if something goes wrong, you have 7 different vendors (and 7 different warranties) and you'd have to send the right part back to the right person if something was wrong. However once the thing is running, it's pretty much going to be fine.
My first computer at home (not the first I worked on):
Atari 400 - $599
Atari 410 tape drive - $90
Old B&W TV set - from grandma
We later got Star Raiders, Asteriods, Defender, Jumpman, Caverns of Mars, etc.