Besides Live One Care you could try a free version of AVG to see how well that works on the 64bit edition. The latest version had no problem going onto the 32bit edition of Home Premium and many 32bit programs may still run on the 64bit edition you have. It's actually trial and error for 64bit since it hasn't seen the support the 32bit versions see.
Since I was not very far along at all into getting everything setup, I opted to go ahaed and install 32-bit instead. I really like One Care and I know I can trust as it has helped me in the past so 32-bit will suffice until I upgrade to 4gigs next summer or so.
You could install 4gb even with the 32bit version being run. Windows will simply take some 3/4gb of memory addresses and map those out to hardwares leaving you with 3.25gb or so of available ram less what loads along with Windows there. But you simply would see any big gain in performance like you would going from 1gb upto 2gb for a total amount. That's the larger step there. 3gb can also work with two 1gb dimms on the primary and one on the secondary.