I never learned to ride a bike. It is my deepest shame.
Any slick tire will work. Get the cheapest 700C tire that is slightly wider than your rim. Any LBS should have something to work for you. Tell them it is for use on a trainer. DOn't pay more than $25 (max!!!) for the tire, though. A little bit of tread(like small channels for water to escape) is acceptable, but nothing more.
THer are also some trainer-specific (not designed to be used for actual riding) tires available, but I don't know what sizes are available, and if your bike has wide rims then there might not be one of these to fit. They are also more expensive than the cheapest slick hybrid tire but are supposed to last longer.
'''96 Litespeed Catalyst, '05 Litespeed Firenze, '06 Litespeed Tuscany, '12 Surly Pacer, All are 3x8,9 or 10. It is hilly around here!
As LarDasse74 noted, any slick or very slightly treaded tire will do and get a cheap one.
The trick to making tires last on a trainer is to have the roller tension adjusted properly. Too loose or too tight will shred a tire quickly. I set mine so a sharp pull on the tire causes it to slip very slightly. If it won't slip at all the roller tension is too high and if it slips easily the tension is too loose.