What do you wish to play game wise? And what is the maximum resolution of your monitor? To give you a serious response, those are the two most important items to address. They help the rest of us determine what tier of graphics card to recommend to you.
ATI does indeed have the edge right now as far as price & performance go. Depending on what you want to play, your Q6600 @ 2.4Ghz (Stock) may limit gaming performance some (it's very sad to say, but true). That's by no means to say it won't play well, but you may not get the fastest performance possible.
Here are the specs on your computer:
HP Pavilion Model a6452fhttp://h10025.www1.hp.com/ewfrf/wc/document?docname=c01324212&lc=en&cc=ca&dlc=en&product=3691066
I do not see any specifications listed for your power supply. We'll need to get details on that to make sure it'll give enough power for a video card upgrade.