Panaracer T-Serv

The sidewalls aren't as tough as the Schwalbes or Continentals but the are light,fast, good puncture resistance and very nice ride. Unfortunately the biggest is 35 mm. The Pasela TG comes in 37mm. These tires are in the price range but the won't last long heavily loaded on rough surfaces.

You're not going to get "quick"(light)/durable/low cost/fat tire. You can get fast rolling/durable.

Marathon Cross sounds like the tire with psi covering conditions.

You might consider two different tires from front/rear.