Man! Where has that PC been, in the bottom of a muddy creek? Take that thing outside and blow the crap out of it and clean it up.
Sorry... back to the subject...
That PC will take a full height card. No need for low-profile or half height card. And if you don't see any future need for the small yellow PCIe x1 slot, you can use a dual slot card. Most folks just let the card cover the unused slot. Right now, your only limitation is your weak power supply... and some other system specs. Until we decide that, the safest bet would be a lowly 19W HD 5450 or something in that range:
http://www.amazon.co.uk/s/ref=nb_sb_noss_1?url=node%3D430500031&field-keywords=hd+5450&rh=n%3A340831031%2Cn%3A!340832031%2Cn%3A428655031%2Cn%3A430500031%2Ck%3Ahd+5450
Obviously, that isn't exactly a gaming card.
Check the nameplate on the side of the PSU and let me know:
(1) +12V rating in amps and (if shown, watts)
(2) Make and model.
(3) If you have a larger PSU you can use, please let me know the same specs of it too. The gfx card capable of modern gaming is the most power hungry device in the entire system.
(4) The processor and amount of memory your system has
(5) The resolution of your monitor. The higher the resolution, the more work the card has to do to render each frame.