You probably have several limitations. Not enough RAM, a mediocre dual core CPU, and a mid range GPU. Now, given your resolution, the GPU probably is fine... although with a single 5850 I was able to play on High at the most and it took two 5850s to play on Very High, but also at 1920x1080.
Your CPU could use some OCing, but it also is probably ok.
2GB RAM is probably holding you back, causing the game to use file paging on your hard drive, and whenever it has to access it you get lag.
I would think that yes, 4GB of RAM would make your system a lot smoother in games. In a few games, I've had my Task Manager open and looked at the performance and I've used up to 3.8gb RAM in some games. StarCraft 2 and STALKER are using a lot.
Basically any Socket 775 CPU will work. You could go with a faster dual core if you want, they're generally cheaper. Depends how long you want it for, as quad core will have more and more support in the future.