Do not buy a HP computer. My first PC was a HP computer (10 years ago) and it was a very poor experience. It does not last for long and they put very low quality hardware in it and charge quite a lot.
Personally I love HP and Toshiba. We even had a HP printer/scanner and it lasted longer than we thought.
However I've never tried their gaming computers; I'd assume they just have a faster processor and hard drive with the needed graphics card to play most games. You'd probably be better off just making your own computer. 😛
I've only one experience with HP and it was a white special edition HP laptop. That computer lasted me 6 years until the buttons started popping off. lol
As far as gaming goes.. it handled The Sims 3 really well. 😉
If you are looking for a gaming desktop, I recommend either assembling it yourself and buying the parts, or buying one from iBuyPower or companies that do custom/gaming computers.
Don't buy gaming computers from Dell, HP, Toshiba, Sony, etc. They are usually more higher priced for what it's worth.
I recommend assembling the gaming computer yourself. I have built my first gaming computer a few months ago, and I learned a lot about computers, and it definitely saved me a lot of money. Plus you don't have to pay for labor fees.
EDIT: Plus you get warranty for each part, instead of sending the whole computer.