Just to clarify, the slot you will use is the PCIe not the PCI, it is a x16 one (it is full length), and it is a PCIe 1.0 (first generation). It is relatively slow, but the CPU is going to limit game choice much before you actually saturate it.
A much more important question is what is your PSU (the box powering the computer)? How much power does it generate?
More modern cards need more power than what you have now. THis page
has a list of graphic cards (and it's a trusted place, that reviews such cards since a long time ago). The more powerful at the top, the weaker at the bottom. Use this as a compass to find the more powerful card you can buy with your budget.
For your rig, any card with more than 1 GB is overkill, GDDR5 is faster graphic memory than GDDR3 (better 1 GB of GDDR5 than 10 of GDDR3), but again you can live with GDDR3.
That said, you can aim for the more powerful you can find without wasting money.