[quote name='DrFoo']$500 should be enough. Here's a build I made really quick just by looking through newegg:
Motherboard:
Foxconn G31AX-K $50
Processor:
Intel Core 2 Duo E7400 Wolfdale 2.8GHz $120
Video card:
ASUS EAH4850 TOP/HTDI/512M Radeon HD 4850 $110
Memory:
CORSAIR 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 800 $30
Hard drive:
Seagate Barracuda 7200.10 ST3250310AS 250GB 7200 RPM 8MB Cache SATA 3.0Gb/s $48
DVD Burner:
Pioneer Black 20X DVD+R 8X DVD+RW 12X DVD+R DL 20X DVD-R 6X DVD-RW 16X DVD-ROM 40X CD-R 32X CD-RW 40X CD-ROM 2MB Cache SATA 20X DVD±R DVD Burner $23
Power supply:
Thermaltake Purepower W0100RU 500W ATX 12V 2.0 Power Supply $35
Then just look through newegg's
computer case section and pick out any ATX case you like and you should be set depending on what inputs your receiver has (this setup has DVI output which can also be converted to VGA if necessary, but you might need a sound card for your audio). It should come out to about $450-$500 and I'm sure it can run any game out there on fairly high settings. Then as far as actually building it, motherboards usually come with fairly good build instructions or else you can google build guides. Also if you need a copy of windows I think it costs a little under $100.[/quote]
Few things that struck me in this build.
Depending on the amount of Video recording he wants to do, he may want to slap in a bigger and/or another hard drive. Or maybe get some externals. Either way, 250gb will probably be used up fairly quickly.
Also of note - with 4GB of ram, some will be wasted, unless you get a 64-bit OS. With a normal 32-bit system, your computer will only read ~3.4 or so GB of ram. It's not worth going for cheaper ram to save a few bucks, as you won't save much, but it's something to be aware of when you're setting up your system.
The OP also mentioned a desire to do light gaming. As i'm willing to bet everyone on this forum can attest to, if you have a choice of playing a game on PC or on 360, the PC version is usually better. There are some exceptions, but in general, a PC game has a lot of benefits over 360. Easier to Mod, get updates faster, don't need to pay for Live to play, usually easier to find and get into a game...the most blatant example is Team Fortress 2. Compare the achievement packs and class updates PC has gotten with what the 360 has gotten.