According to Acer specification, your PC has good potential. However, your current situation is quite undesirable. Any graphics card that fits in you current case [assuming your current power supply can handle it] is a BAD investment simply because of extremely bad "price vs performance ratio" - which translates to poor performance improvement in practice. Also, I wouldn't trust that PSU either - there is a 99% chance it's a brandless OEM unit.
You have two routes.
The first to get a bigger case before getting a new Power Supply and Graphics Card. [Hard to quote budget due to too many hardware possibilities]
The second is to get a power supply and a graphics card that fits your current case which will give "worth-while" performance improvement [Under $80]
If you still want to get a graphics card for your current PC without a new case, you'll need to at least:
a) Get a new solid PSU
b) Measure your PCI-E slot clearance [Can probably fit a ATI 5670 - it's a entry level graphics card but light-years ahead of integrated graphics in performance)
GPU ATI 5670 1GB Link ==>
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150535 [Under $50 after taxes and rebate]
PSU Mirco Diablotek 380W Link ==>
http://www.newegg.com/Product/Product.aspx?Item=N82E16817822001 [Under $35 after taxes]
Side Note: I'm guessing with your current case it can probably take micro PSUs, I doubt it can take a standard ATX form factor PSU.
~Coffee
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