There are 3 factor you have to look for when finding a suitable graphics card. I just simplify what mvweez1 said.
1) CPU. When choosing a GC, we have to look if it's compatible with the CPU. There are no specific ways to tell that, so we have to use logic. A newer CPU usually compatible with newer GPU. In your case, you have an i5 2300, so most newer GPU is compatible.
2) The slot. Newer graphic cards use PCI-E X16 slot. You have to find out if your motherboard have that slot. In your case, your motherboard have one.
3) PSU. PSU is the most important factor when choosing a GC. High end GPU use lots of power, so a bigger watt PSU have to be use. In your case, you have a 300W PSU, so any GC without a power connector can fit in. But, I recommend you to upgrade your PSU to atleast quality 500W PSU (Antec, Corsair, SeaSonic, XFX) and above. You can find one about $40.
Now, we only want to know your GC budget.