Although many other tires would also do, you cannot go wrong with one of the tires in the Schwalbe Marathon line. Yes, the Marathon Plus is heavy--too heavy for some and not too heavy for others. You can save considerable weight if you give up slightly on flat protection. Other tires in the Marathon line such as the Dureme, Mondial and Supreme are lighter and almost as flat resistant.
The only tire in the Marathon line that I would shy away from, if your budget allows it, is the tire referred to as simply the Marathon. This tire is much less expensive than all the other tires in the Marathon line and is less reliable. Read the descriptions that Schwalbe provides and choose a tire suitable for your needs. You won't need an off-road tire for the TransAm, even though you may find occasional need to go off road (e.g., to a campground).