Physical RAM restrictions of operating systems in Off Topic
if you install 32bit you'll have only 2GB or even less.
RAMs are pretty much last, the more memory GPU has, the less RAMs will. That GPU has 700 MB more than mine, so that PC will have 700 MB less RAM.
For games I'd say even Dual Core is enough, but Quad surely will be better.
But I think you might need little better Video Card, it's kinda low on bits =/
Please keep in mind, with 4GB RAMs you'll have to use 64bit OS, if you install 32bit you'll have only 2GB or even less.
Where does it say 3GB?
When I had 4GB and 32bit Win7, in Computer Properties it was saying 4GB (2.7 GB usable) also in Task Manager total memory was 2731 MB or something.