Why don't you start with dropping the rear wheel, and measuring the distance between the inside of the dropouts?

If the distance is 126mm (based on your guess as to the age of the bike), then you can use a 6/7 speed rear wheel.

If the existing rear wheel is 126mm, all you need is a new 6-speed freewheel to run a 6-speeds.

If the existing rear wheel is 126m and the frame is 126mm, then you can buy and run a 7-speed freewheel, but you will have to buy new 7-speed shifters to run indexed, OR run in friction mode (with your ols 6-speed shifters) all the time.

If the existing rear wheel is 120mm and the frame dropouts are 120mm, then you will have to run 5-speeds and friction/non-indexed shifters. Unless you want to have the frame respaced, buy a new 126mm rear wheel, decide whether you want to run 6 or 7 speeds, and buy 7-speed shifters if you are going to run 7-speeds.