To be honest asking for a gaming rig and then wanting a quad core is kind of an oxymoron and then for under $600 your really asking for too much.
The x3 720 is a great proc and will do fine stock but if you have even a little know how you can easily over clock this rig to a good 3.4 GHz on a decent 3rd party cooler
The PSU is by Raidmax and although not a top notch PSU it stills fills the void of good quality without breaking the bank
that's the "nVidia" version, I couldn't find the regular one.
$650 just seems to be the best your gonna get without gimping parts (not an option) but this list come with $50 in rebates as it is so take it how you want to it can come close to your $600 budget after waiting a month or so for rebates, my suggestion would be to just save an extra $200 or so and then you'll be in line for a nice build
ey for the motherboard
depends what your using the computer for wouldnt you try to get the asus rampage ive heard great things about it, but also depends on the budget i suppose
ey with ya hdd go raid with it dont go the single 250gb. go two 125gb it might quicken the computer up and less wasted time, only the budget might suffer there though