Thinner tires for my Mountain Bike
What you want for road use is slick tires -- tread and knobs are bad for road use. You have 26" (ISO 559) rims, so you need 26 x (something) tires where (something) is a number in decimal form (e.g. 1.75). 

Going for smaller tires will lower the bike a bit, and smaller tires have to be run at higher pressure (so you'll get less cushioning). There will also be changes in rolling resistance (You may want to read the whole "Tech Info" column on the right side of the Schwalbe page).

As for how small you can go, technically you can mount pretty much any 26x(something in decimal) tire on, but the rim width should ideally be of the right width so the tire doesn't roll off or increase the risk of flats or rim damage. 

I'd probably look at something with a puncture protection belt, like the Schwalbe Marathon Plus (26 x 2.00 will likely be one of the larger slicks they sell, and you can likely go narrower depending on the rim width).