First step is going to get to get the POS PSU out of that machine and replace it with a good power supply. Compaq is still using PSUs with passive PFC which is a sign of an ancient design that isnt built for this era of hardware. HP tends to cut it as close as they can with their power supplies and unlike dell their low end units are the cheapest ones they could buy. You can get an Antec EA430D for $47 after promo code to replace your current unit with.http://www.newegg.com/Product/Product.aspx?Item=N82E16817371034&Tpk=ea430D
Once you have that installed as a nice insurance policy so your components arent at risk of an overstressed PSU, then a 5570 would work quite well, or a 5670, both use fairly little power, arent super expensive and will provide moderate performance for games.