If you can see inside the case, please verify the existence of a PCIe slot with clearance for a full sized card. There should be gt720 card in the slot now.
Depending on your PSU power rating and possible lack of a dedicated 6 pin gpu power connector your choices may be limited. You may be looking at a gtx 750ti or a non-overclocked rx460. Either of these would be a great improvement from what you have now.
Yes it is a turbo link 350 watts. Pretty much a garbage power supply according to the YouTube videos. I would like to change it out to a corsair cx 750. Is that too much power?