Help in upgrading a pc.

[ThermalReaper]

So, I've talked to Goku a bit and I guess I've found a good and cheap GPU that would work fine with the games I'm unable to play in this current form of my PC.
Would the current PC support: Radeon HD7750? And if not, what would I need to upgrade?
Another few GBs of ram when I eventually upgrade to 64 bit?

Specs:
Amd phenom II 710 X3 2.6 ghz
3 Gb of ram(DDR2, don't know how many sticks)
32 bit windows 7
Gigabyte GA-MA785G-UD3H
450 Watt psu(Don't know model yet)
And the piece of garbage I'm sure is making me unable to play games:
Amd Radeon 4200 HD.
As for resolution, I'm considering in the range of 1024x800 to 1200x1024

The games I'm unable to play:
Tribes ascend, black light retrubution: Absolutely terrible 11-17 FPS even on 600x400 and tweaks, barely playable.
Splinter Cell conviction, mirrors edge and dragon age origins: 25-19 FPS, playable, but barely fun compared to playing on my brother's laptop.
Sniper Elite v2, Crysis 1 and 2, The Mass effect series, The F.E.A.R Series, The Assassins creed series, borderlands, Deus ex:Human Revolution, and Bioshock: Unplayable. The maximum I've seen was 5 FPS.
My computer barely overheats and the only time I've truly felt that it needed a rest was 3 or 4 years ago, on a continuous week of 40+ temperatures.
I usually have on low settings but I don't want to max anything.
Also, is it worth it to upgrade my PSU a bit to support a 7770?