That's what I did with my Trek 1100 that my dad bought new in 1990 and passed to me a decade ago.

Actually, I have a mixed set of components: used 105 RD and Ultegra FD, Tektro front brake, something-or-other rear brake, and FSA crank. But I bought some new 105 levers (5700--ten speed). With this stuff and some decent wheels, the bike has gained a new life, and I expect it to give good service for another 20+ years.

Enjoy your rebuild!