Couple of questions.
1) Does your current motherboard allow overclocking? Because that i3 530 has Hyperthreading so it will behave closer to a quad than a typical dual. And, it's from the last generation of Intel chips that allowed FSB overclocking, so it's the equivalent of an unlocked chip. Should be relatively easy to get it to 4GHz or even higher, at which point it will handle most gaming requirements pretty easily (except for the few games that are heavily multithreaded).
2) What model is your PSU, and/or can you give us the amperage listed on the 12V rail(s).
If you can overclock the CPU and you have a strong enough PSU, I see no reason initially to upgrade those parts, just drop in a new GPU and enjoy some much faster gaming. For 1600x900 resolution, the 750 Ti would be nice, or you could look back at the previous generation and pick up a cheap 660/660 Ti.