Gateway PC upgrade?

I am currently awaiting the arrival of a completely free Gateway PC. Gateway DX4860-UR28 is the model. I am getting this new computer for free because of a lawsuit over malfunctioning floppy drives in a Gateway PC that my parents bought back in early 2000. I have been waiting for somewhere around three years to build my own gaming PC and upgrade from this Celeron pile of junk. It will be a long time until I actually get my gaming PC. This new Gateway will still be quite a preformance increase from my current system. The system has an i5 and 8GB of RAM. I thought if I added in a decent graphics card, I could make it a decent gaming system. My question is, would I need to upgrade the PSU it includes, and if so, how many Watts in the new one would need if I put in a 7770.

you lucky bastard

according to this it has either a 300w or 500w PSU, if you can take a picture of all the stickers on it, we can tell you which one you have

if you have the 500w maybe, it really depend on how many amps and rails it has which the stickers will say

more than likely you'll be able to put a 7770 in on the 500w one but I'd still like to have a look to make sure its not REALLY crappy