I was in a somewhat similar situation with a '88 Trek touring bike and decided to keep the bike (that was years ago though, and now I am ready to move on).

I'd suggest just doing the bare minimum. I'm sure the rear is spaced 126mm and replacing the wheel will be a little more involved than just mounting a new one. If the existing wheels are 27", you may also have issues with getting the canti's properly adjusted with 700c rims (I did on my Trek).

I ended up replacing the 6spd indexed downtube shifters with 7spd brifters and a new freewheel, as well as replacing the brake pads.

Check out the cog spacing page on Sheldon Brown's site to figure out compatibility,
http://www.sheldonbrown.com/cribsheet-spacing.html
but you might be able to use a set of Shimano bar-ends (I've got two pair of 7spd bar-ends, and could make you a great deal on a pair, though am sure there are others out there as well) with your existing (Suntour?) freewheel, though I'm sure you'd need to change to a Shimano derailleur as well.