Appropiate graphics card?

[Cyadd]

So, since I'm doing this for a friend, and he doesn't know (or doesn't lead on about this stuff) much about upgrading, and that I'm only diving into this stuff, and that he has an onboard graphics card, which is the sucks, he wants a graphics card that is cheap (-$45), contains an HDMI port, and works for a PCI express x16. I've been able to obtain this information about his system:
GIGABYTE TECHNOLOGY
S series motherboards
GA-965G-DS3
Supports core 2 duo LGA 775
PCI-Ex16 graphics interface
PCI-E Gigabit LAN
Dual Channel DDR2 800
SATA 3Gb/s interface
3*PCI-Ex1 and 3*PCI Interface
Supports up to 10 USB 2.0 Ports
Intel High Definition 8 Channel Audio

Now, the card I spent 5 minutes finding one was this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121259

Can anyone confirm that that card would be satisfactory for his system? He would probably need to buy an HDMI cable. He also said something about not having a fan to cool off the heatsink, which I don't think would be a problem.

Thanks for everyone's help. (If you also find a better one for cheaper, or if it wouldn't match his specs, don't hesitate asking. I may make his /run dxdiag for more things if needed.

[XTOTHEL]

it's a rebate but you'll/he'll get the money soon or later :S http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3592052&CatId=1558

also getting a DVI to HDMI adapter would give you more options in cards than requiring it to have a built in HDMI port

[Cardboardsnail]

http://fxvideocards.com/ZOTAC-NVIDIA-GeForce-8600-GTS-DVI-Audio-256MB-ZT-86SE25P-FSR-128-bit-GDDR3-PCI-Express-x16-HDCP-Ready-SLI-ZOTAC-Video-Card-p-16304.html

It comes with a DVI->HDMI adaptor as well

I'd go for XTOTHEL's suggestion if he games at high resolutions though
(Make sure his PSU can handle the 8800GS if you do decide to get it)