What kind of power supply do you have? Also, a little more info on your computers specs would be helpful. I.e. CPU, motherboard, HDD, PSU, Current GPU if any. What do you plan to do with your new graphics card? What games do you want to be able to play? What is your actual budget range? With a 1.8 Ghz Dual core processor you probably have a PCIe 1.0 slot, is that correct?
Based on the very limited info. you have given I would suggest a Radeon HD 6670 or possibly a Radeon HD 7750 based card.