Based on your 250 watt power supply and case size, the best upgrade is going to be something like a low profile model AMD RADEON 5450 OR 6450. They are very low end cards these days made mainly for HTPC applications, but they will be a significant improvement over your current graphics.
Not really sure about the 1gb issue. Never heard of that.
I agree with the 2gb ram upgrade also. It is very cheap right now.