The way video cards go, the 1st number is the newness... ATIs go 3xxx, 4xxx, 5xxx Nvidias go 6xxx 7xxx, 8/9xxx, Now its... gts 2xx 3xx gtx 4xx
The second number is how good it is, so a 4870 is better than a 5350 in ATI, and for nvidia its weirder due to how they renamed products... a 9800gtx+ is alkso a gts250, but the general thing is higher the 2nd number, the better it is.
Now, the hp you linked is okay, but the ATI 4200 is not a true video card, as it is built onto the motherboard, and uses the RAM from the system. It should play it, but how well will be the issue, its not great.
You could add a stand alone card, but could easily be an extra $100.
As Sean said building can be better, especially if you have an old one to reuse parts from, like keyboards, hard drives dvd drives etc. But building at your 5-600 budget can be tough as Windows 7 is $100 itself.
If you have to go with a prebuilt, like the HP, I'd go this one for $50 more: Gateway Intel Core i3 540 Computer (DX4840-01C) - Future Shop Exclusive - Future Shop
Welcome to TF, hsve more questions....ask away