Hello and welcome to LQ!
1. Am I correct in assuming that all programs written for Linux will run on any version of it? It seems to me that the ďtrunkĒ of the tree is Linux with a lot of branches like Debian and SUSE.
Depends.You can compile software from source if you wish, which will work on most systems.However it's normally easier to install software via a package manager ie aptitude for Debian or Yum for Fedora.
Debian and Suse are distributions of Linux,which is a collection of software with the kernel at it's core.
2. Which version would run on my future AMD machine and give me a 64 bit OS? Iím leaning toward Debian.
Debian is an excellent choice for a 64bit o/s.
I would recommend the net-install version,here's a link:
Install the standard system,don't select desktop from the installer.
Then install xorg and a desktop environment manually, for a nice lean installation.
3. Can someone narrow down the hundreds of Linux versions to maybe 5 or 6? I will do the legwork myself and read the forums but right now I have too many versions of Linux to plow through and need to short list a few.
Other disto's worth considering would be Slackware or Gentoo .
Hope this is of some help.