You have forgotten to mention the most important component the motherboard.But I am guessing that your motherboard has a PCI-E slot for your graphics card. Although you have mentioned a limited budget,how much is that exactly? What sort of games do you play?
Use this SIW. Scroll down to the free version,download and install and then open the program. On the left hand side under Hardware you will see a Motherboard heading, click on that and on the right hand side you will see, under Summary your motherboard maker and model.
Sorry should have asked what size power supply have you,you will need to take of the side and have a look and it will say,I think 350/400W. Can you check as that also makes a difference to your upgrade choices.