This is the red bike you posted in the cycling thread right? Those are almost definitely 26 x 1 3/8 tires. You can get them at any shop that deals with older bike repair- Bike joint will have them for sure. You won't be able to measure anything accurately. If you don't want to make 2 trips to the bike shop, just bring the wheel and test fit the tire when you go.
You are correct on the rim tape, that is required. You could buy a new rim- and it would be cheaper to buy a pre-built with a new hub but you're going to have to get the same size to fit the bike so it won't make much of a difference on your tire supply. The tires shouldn't be hard to find, and you should be able to get an inexpensive one for $20. $50 for a fancy one.