If your budget permits, buy the GT730 64 bit.
Not only is it considerably faster than the GT230, but it takes less power.
Here is a chart:
http://www.realhardtechx.com/index_archivos/Page362.htm
I do think your psu would run either.
Actually, you could run a much stronger GTX750ti if you wanted on your 300w psu.
In addition, a GT730 could be simply dropped in and use the same nvidia graphics driver.
The AMD would involve replacing the nvidia graphics driver with the appropriate amd graphics driver.
Your graphics slot is a pcie X-16 slot, not a pcie slot.
Pcie-x16 is the norm for all modern graphics cards.
Either card would fit the slot.
If there is any fitment issue, it will be with how high the cards are. If your pc has a slim case, you will need a low profile graphics card.
And... spend some time cleaning out the dust in your cpu cooler.