We have a Advent PC that has 2GB of RAM and a 2.20GHz (I can list full specs if needed) 64bit CPU, on Ubuntu's website it says if you have 2GB of RAM or less install the 32bit version; but couldn't we benefit if we installed Ubuntu 64bit? That way the OS could take advantage of the CPUs 64it instruction set. Any answer would be appreciated.
SnapOverflow
If you have a 64 bit CPU you can install a 64 bit version.
The 32 bit version of Ubuntu needs only 512MB RAM, the 64 bit version will need a minimum of 1024MB RAM. Since you have 2024MB RAM (2GB) you can install the 64 bit version on the 64 bit processor.
If you Installed Latest ubuntu 13.10 64 bit and get into any trouble just get the previous version (e.g 12.04 or earlier) those version deal with less RAM and your computer will be fine