For recording only, he can get by with a decent dual core system. You're asking for way too much for such a small budget. Why are you building a dedicated computer only for recording from your 360? Why don't you just get a game bridge and use that?
Okay, the performance isn't dependent on your hardware. The gamebridge basically uses your computer as a t.v. which you can use to record directly. The Phenoms are so bad at editing, you might as well go with a high end Core 2 Duo.