You will be fine putting a 7750 in there. I am a little iffy about recommending a 7770 though. Don't go with a 630, the 7750 is a great compromise between the 630 and 7770. Technically, you would be fine putting a 7770 in there (you won't even reach 80% of max load on your PSU), but I know your psu is old if you've never replaced it before. I'll write out a little math to help:
80% of PSU max output: 240W (I choose 80% because most power supplies work well up to that point. After that they tend to lose their efficiency and have to work much harder to output just a little more wattage/power)
Your system w/out GPU: ~100W (or less)
Your system w/7750: ~150-160W (gpu power draw 50-60W)
Your system w/7770: ~180-190W (gpu power draw 80-90W)
Regardless, I feel like you should avoid trying to put a new power supply into that machine unless you really do plan on keeping it for a couple more years. I noticed its a PCI express 1.0 slot and that tells me your computer is not really worth putting much more money into. You will be able to game at medium to high settings, depending on your monitor's resolution.
Do not buy anything more powerful than a 7770 though, even if you do buy a new psu. I think the rest of your system would hold back the gpu's performance anyways.