The Vittoria Randonneur Touring tire comes in a 700x38 and is known for its value, durability and ride. The Continental Travel Contact and the Schwalbe Marathon Dureme tires are more expensive but widely acclaimed as some of the best tires of their type available.
Schwalbe Marathon ... any one of those is simply superb but also expensive, obviously.
A cheaper alternative are the ones I use: Schwalbe CX Comp ... a lot cheaper and also usable for every purpose and very puncture resistant ... I rode in an actual piece of metal wire and it went in and out of the rubber but couldn't get through the kevlar layer. These come in 28 and 35 ... I don't know whether or not they come in 38.
Kevlar or no kevlar, "goathead" thorns are winners everytime.
Truth. If you see a goathead thorn in your tire, I don't care what tire it is... immediately stop and pull it out. If you don't I guarantee it will puncture any tire made after you roll over it some more and mash it through the casing.