Originally Posted by Bill Kapaun

Front wheels are relatively generic for that era. 100mm spacing & rim brakes.
The rear requires more attention since they come in different "speeds".

Your bike appears to have a 7 speed cassette. 7 speed Free Hubs are shorter than >7 speed hubs.
You MIGHT have an 8 speed hub with a 4.5mm (3/16") spacer installed before the cassette to take up the extra room. You can eyeball this.
drop out spacing is important, but I'll assume it's 135mm (5-5/16"). CHECK to make sure. It might be 130mm.

IF the bike is 135mm AND you are changing shifters, now would be a good time to go to 8 or 9 speed.
You need a new R shifter. IF going to 9 speed, also a new chain.