I did the same thing with the 1988 Univega Gran Touring below.

For first (and maybe last) phase mods, I'd:

-- Switch to a 7-speed freewheel

-- Replace existing brakes with aero brakes

-- Replace cables, housings, etc.

I left the 27" tires on this one and there are a reasonable number of good 27" tires on the market. If you want to go to 700, it's easy to do. And if you do, that increases your gearing options because you might as well go with a Hyperglide hub. Others can comment whether it is necessary to spread the stays.