Resurrecting a family bike must be a great feeling- I'm about to take on that project with my father's Triumph over this winter.
As Bob mentioned, aside from the knowledge base on here, triplesonline.com is a wonderful source. Some of the guys are not the most computer savy, but they certainly know the ins and outs of these triples.
I just rebuilt a 72 Trident last year and did a fairly extensive writeup of the process that you might want to read. http://www.triumphrat.net/members-re...e-project.html
Hopefully you can eliminate some of the mistakes I made during the project...
Post some photos of the bike before you start, and update this thread as you go!
They have their quirks, but they are certainly a blast to ride!