" I just got a 64-bit Windows 7 Pro machine, which will connect with any machine on my home network as long as it is also Windows 7."
I have my XP networked quite happily with my Win 7 Pro laptop - if I remember how I'll let you know.....
It is possible to load a the FTM program on a second computer - it worked for me. You can access the FTM trees via the network.
To transfer the tree to the new computer do a MANUAL backup to produce a zip file with .ftmb extension - it contains the .ftm file and Media folder containing all the media files. Copy this to a suitable folder on the Win 7 machine and open with FTM, locally or networked, saving the .ftm in a suitable location.