Hi Chris, and welcome to the Forum!
Others will no doubt have their own ideas, but I'll go out on a limb here and suggest visiting a Trek (!) dealer to check out the available Bontrager tires. Most are pretty inexpensive as tires go, and I've found them to run true and round, (de)mount easily, and to have lots of grip and puncture protection regardless of price. They're inexpensive enough to play with if you want to try something without making too much investment in rolling stock.
I've had exceptionally good luck running Bontrager Select K4 (Kevlar-belted) road slicks in 700x32C on my rando bike. Essentially a slick, (there's some small, shallow "character lines" on the shoulders), they grip well when cornering deeply on wet city streets. I paid about USD$22 each at my LBS for the wire-bead model. Unfortunately, this particular model is no longer available; Bontrager have overhauled and renamed their line for this Spring.
The T2 looks to be the replacement for only USD$2 more, if you wish to experiment on the cheap:
http://bontrager.com/model/08861They don't last too long under heavy touring (the rubber wears "square" on the center tread under very heavy loads), but last a good long time when riding unladen or with day-ride loads and resist broken glass particularly well.
Just another data point if cost is a prime factor; they work as well as many more expensive tires.
Best,
Dan.