It appears to be a sturdy and serviceable bike, but, if it were mine, I wouldn't put a bunch of money into upgrades. Service the bearings, do the cables, brake pads, maybe a saddle to your liking. True the wheels. New chain and freewheel (maybe go to a 7 speed if the frame spacing in the rear is 126 mm). Clean it up, wax it, ride the heck out of it, and save your money for something better. IMO, your effort and money would be better spent making the bike in its current configuration as pretty and well working as possible. Some solvent, grease, aluminum polish, and work and you can have that bike looking and performing as well as it did new -- maybe better.
If it's friction shift (I assume it is) and you want indexed, going to a "modern" 7 speed freewheel and selecting a relatively inexpensive Shimano 7 speed compatible rear derailleur (most of them will be) then you just need some indexed shifters. Indexed 7 speed down tube shifters are probably ebay available for not much. You can get 7 speed brifters, too, but that may be a budget buster -- I don't know.
In the late 80s, Suntour had a 7 speed indexed system called Accushift (I think). It worked very well, in my experience. Maybe that stuff is available relatively cheaply, though it would probably be down tube shifters.
Probably going to 8 speed or more, which would require a cassette hub,
afaik, isn't worth the expense.