It went so smoothly that I almost forgot to post about it, but I upgraded my server last Friday evening.
I moved up to the latest version of Debian, went from Apache 1.3/PHP4/MySQL4 to Apache 2/PHP5/MySQL5, and got rid of a whole bunch of applications and services that I had installed to play around with but don’t need anymore - stripping it down to the bare minimum. E-mail and DNS were not changed, just updated.
So far, so good…