Does that $500 price per PC include Windows, monitor, keyboard and mouse? Or, are you just replacing older systems and can keep all those with just replacing the computer tower itself?
If you need everything, then the practical choice is to find a hot deal on a name brand system with a PCI-E 16x slot for $400 or less, and add a $100 video card. There has been a few deals on the Dell Vostro 200 and 400 series in that price range. Also, many of the current AMD chip systems have PCI-E 16x slots.
If it is $500 for just the tower and not including Windows, monitor, etc., then building your own can be a reasonable choice. Here's a rough parts list - you may or may not be able to do better pricing depending on hot deals or rebates:
CPU dual core AMD or Intel $75
HSF (use what's included in retail box)
motherboard Nvidia or ATI chipset micro ATX socket AM2 $70 OR Intel G33 $110
RAM get cheapest DDR2 800 $45
HDD cheapest 160-320GB $50
optical cheapest DVDRW $30
case/power In Win micro ATX case with 350W power supply $70
video Radeon 2600XT or Geforce 8600GT $120
= $460-500
If you go with the AMD setup you will have close to enough budget to go with the Radeon 3850 (with perhaps better PSU). I know AMD is not the "popular" setup, but trust me it works and plays games just fine. I kept some mild overclocking in mind. If you are absolutely NOT going to overclock, then you can get by with a $50 motherboard for either AMD or Intel platform, and if NOT overclocking then at the same price point it doesn't matter which you choose. Otherwise, with Intel you have to pay more to play at overclocking, but you may have greater returns in performance.
Now, some people may argue with me on the case/power, but within your budget for both dollars and power requirements, I think the In Win units are sufficient. It's tough to justify $80 just for the power supply on a $500 computer. The In Win PSUs should work okay for such a low power draw computer, which will probably pull around 150W from the wall at load. An alternative is the Antec NSK3480 which comes with an EarthWatts PSU which should be sufficient for such a system setup and any video card needing only one power plug. That case/PSU costs more though, +$20-40.