This site has a rather extensive comparison of the various flavors of Linux. The release notes here might also be useful.
Since it is going to be installed on a home computer, I would choose the latest version (8.10) which includes new features (such as 3G wireless support).
If it was for enterprise use, I would probably choose 8.04 LTS (Long-term support).
Personal opinion, it comes down to what you want: Stability, or, theoretically performance and the latest features. 8.04 is more stable, as an “Long Term Support” option. 8.10 is more cutting-edge, although they do not add what would be considered “unstable” software.