Make sure the manufacturer didn't disable the ability to crossfire. According to the HP website they state "Either integrated graphics or the PCI Express x16 slot are usable at one time; they are not usable concurrently"
I have that issue with the a8-5500.
You dont state your powers supply's wattage so I will assume its the a8-5500's standard 300w. This limits you to the 7750 without upgrading your power supply. The 7750 is a good card and will keep you under budget as well as give you a good frame rate in most games.
The downside is you MUST upgrade your power supply if you want to get a better performing card at a later date.