Congratulations! It sounds like you have a nice system.
I started out with the 32-bit version because it was my first time with Ubuntu (and Linux) and that was the recommended download, but after using it for awhile I decided to see how the 64-bit version would perform (I had the RAM and the processor for it). I found that the 64-bit version was sometimes slightly faster, and it has been very stable (so was the 32-bit version). I have been told that there are a few things that don't run on the 64-bit version, but I haven't found anything that wouldn't run on it except for one piece of hardware.
It was a Linksys USB wireless antenna. Finding the 32-bit drivers had been tough and then installation was somewhat involved (for someone new to Linux), but it worked. I could not get it to work at all with 64-bit Ubuntu. Fortunately, I didn't really need it and so have been pleased to stay with the 64-bit Ubuntu.
However, you should be careful of such things. If you have room (and I imagine you do), install 64-bit Ubuntu alongside the 32-bit version and see if everything works, and it'll also give you the opportunity to compare speed and stability.