Newbie looking for Graphics Card, Please help

Hi, I'm pretty much a newb when it comes to computer stuff, but i just bought this computer Computer and I want to upgrade the graphics card but I'm not sure which cards are compatible with my computer. I tried doing a little research to find out information about graphics card, but I didn't find much useful information. I would like to know more than just a list of graphic cards that will work. I'm wondering what feature of the computer determines what graphics cards are compatible. Also the monitor that I have is this one Monitor Thanks in advance for any input.

The PCI-Express slot determines the kind of card you can use. Pretty much, you can use anything made within the last 4 years.
Secondly your powersupply matters as well. The site doesn't say anything about yours but im assuming its pretty decent.

If you want to play modern games at native res and lots of detail, buy the 4870 from ATI. about $250.

if you don't have that much cash (skeptical about that) then you can get the 4850 from ATI. That is running wel under $200 nowadays.

Have fun!

The weak link is your power supply according to HP it is 350 watts but they do not specify Amps on the 12 volt rail.

If you just want cheap, I'd say go for the 4670. However, you have the cash, might be worth it to upgrade your power supply and go for a 4850 or better.

probably not. Most HPs iv seen are standard ATX

A coupleof links that should help. The first shows how many watts each graphic card will use at load.
http://forums.atomicmpc.com.au/index.php?showtopic=264
This one helps calculate how much power your system will use and what size power supply to get.
http://extreme.outervision.com/psucalculatorlite.jsp
Most manufacturers recommend running your power supply at 60% of it's rating at load. This is the point where it's usually most efficient and helps for it's longevity. To help in cooling your best choice is to get a graphic card that exhausts hot air out the back of the case. With a prebuilt like a HP it's worthwhile to get the best cooling solution for any high end graphic card. With your monitor i'd seriously consider getting the HD4870 1GB or the GTX260 216. Download hardware monitor and record your temps at idle and at load now, after you add the new power supply and graphic card keep an eye on your temperatures. You may need to add spot cooling, a case fan (tough to do on a HP) or PCI slot cooler. Any quality 550w power supply would be fine for your use. Corsair, PC Power and Cooling, Seasonic or Antec among others.

Thank you very much everyone for your help. I will follow these recommendations and get the 4870 and get a power supply above 500 watts. Thanks again for the help.