That HP computer you posted is not bad, the only uncertainty is the refurbished part. You don't know what was wrong with it and refurbished computers generally come with a limited warranty to fix future problems. That being said, assuming all those components work that would be a very good deal for the HP computer.
However, if you do decide the route of building your own PC, this is what I would suggest trying to keep you at a budget of no more then $700. I would also suggest investing in a better case and power supply in the beginning, so if you ever decide to upgrade/replace/add-on you have the bare essentials already:
Microcenter this Friday & Satuday only i5-2500k for $150. Hell of a fucking deal.
http://slickdeals.net/forums/showthread ... &t=3367862
Radeon 6850 I've seen for sale as low as $100 After Rebate. Right now it's averaging about $130
Here is one for $115 after $20 Rebate and it comes with Deus Ex:
http://slickdeals.net/forums/showthread.php?t=3361372
2x4GB DDR3 RAM I've seen go as low as $30. Nothing really good out there at the moment.
Corsair M4 SSD 64 GB $90 when on sale. You said you are currently using a 500GB HDD which you can also transfer over.
DVD/CD Burner no more then $20 but more then likely you can already carry over the one you have.
Case probably don't need more then $50. Suggestions:
Antec 200 V2, currently $30 after $10 Manufacturer's Mail in Rebate(MIR):
http://www.microcenter.com/single_produ ... id=0334132
Antec 300, currently $45 after $10 MIR
Power Supply:
620 Watt Antec $50 after $15 MIR:
http://www.microcenter.com/single_produ ... id=0348767
Motherboard:
Expect to spend at least $100, no more then $175.
My current recommendation would be a P68 motherboard, specifically a bundle from Microcenter with the i5-2500k:
Combo price for the i5-2500k and a Gigabyte GA-Z68X-UD3H-B3 is $290.
Win 7:
$30 for professional version in my student thread, and if you can't find an .edu address I can get you a Ultimate license for $40.
All those items I listed above come out to $700. You should use slickdeals to find what's on sale, and not buy components unless they are on sale. I would also hold out on the video card as long as possible at least until the 7000 series launches. Perhaps transfer over your current video card until that point or use integrated graphics.