The radeon 7750 needs 55 watts maximum to run and I've read your acer has a 220 watt power supply so it might work.
Upgrading the power supply would be tricky because there's not a psu that will fit perfectly.
I recommend trying the 7750 first because if the power supply can deliver atleast 200 watts it should be ok.
Sorry zeebolt, I don't suggest spending any money on upgrading that computer.
Maybe try to sell it when you got more money?
It's a good basic PC so you could get a hundred dollars or more out of it to buy yourself a better one with a decent power supply and space to upgrade a graphics card.