What size of slick tire should I buy?
Everything you could want to know about tire sizing is here, including recommendations of how wide a tire should go on how wide a rim. In your case, you will look for tires made for 26" rims (ISO 559), but generally, narrow rims should have narrower tires than wider rims. These tires will be marked 26 x decimal number (by decimal number, i mean a number written with a decimal point).

Schwalbe makes a 26 x 2.00 inch Marathon Plus which would probably make a good replacement (the fatter the tire, more cushioning), as well as 1.5 and 1.75 inch variants. A bit smaller of a tire will technically reduce weight (and lower the bike slightly) and give a bit better handling. If you go down to your bike shop, they probably have a bunch of tires which work for the road well. Look for kevlar belting for puncture protection. 

Also, if you're pretty much always on the road, and are running a suspension fork, you may want to swap it out with a suspension corrected rigid fork, since you don't really need suspension beyond the tires on the road unless you have a back problem or something.