The 6150se is an integrated gpu not meant to be able to run games.
I would suggest purchasing a low profile radeon 7750, do you have a PCIe x16 slot on the motherboard and a low profile expansion slot in the back for it?
A low profile Sapphire Radeon 7750: http://www.newegg.com/Product/Product.aspx?Item=N82E16814202002
A PCIe x16 expansion slot on the motherboard: http://cdn.avsforum.com/d/d5/d50b9d8b_800px-pci_und_pcie_slots.jpeg
Expansion slot comparison: http://www.serial-cards.co.uk/SC/media/glossary-images/form_factor-138f91a8.jpg
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.
If it doesn't work out you can upgrade the power supply with this: http://www.newegg.com/Product/Product.aspx?Item=N82E16817104145
(If you're willing to use some tools, maybe even powertools) And try get the screw holes on the case to fit the new power supply.
If you can get it to work with the low profile Sapphire Radeon 7750 it will give you a very stunning gaming computer for such a low price and small case.