I bought a Traxxas Stampede a few years back for the kids to run. It can do all of the above, but I'm not a big fan of mudding because of the cleanup (take that how you want).
They repair fairly easy and the parts are reasonably priced. I've ripped some of the joints out with some of the jumps and straight on collisions that have happened.
Powerful and fast, but now normally only comes out for camping trips.