More important than the tires themselves is how you inflate them. A slick or semi-slick will need much more air pressure than your old knobbies... you'll have less rolling resistance and a smoother ride and a bike that handles better.
Lots of sound advice here. Get the $60 tune-up. Consider getting tires with a Kevlar belt, even though most of my punctures have come from sidewall nails and pinch flats (under inflation, my bad).
My favorite city/atb tires are IRC Metro Kevlar slicks (I run 1.5" and 2") and Continental Town & Country, 1.75" (bike cops like 'em, too).
Oh, and before you hit the road, study this site. I promise you it will make you happier and safer. http://www.cyclingsavvy.com/