The frame will dictate a few things:
-the rear width. If 120, you are not going to be upgrading to really modern stuff without a proper cold set widening.
-the bottom bracket shell. Not a huge limiting factor, but important when it comes to getting a crank set.
-seat post size. Again, limits the selection.
-wheel size. Easily remedied to go 700c from 27 if you use longer-reach calipers.
-calipers. nutted or recessed will make a difference in the selection available.
-shifter positioning and cable routing. early 80's may route above the bottom bracket shell with a piggy-back shifter mount. This all makes a difference, so find out and avoid surprises.

Sounds like fun, though.

Tell us or show us the frame and we're much more able to advise.