Hybrids and MTBs have a lot in common, just differ in weight, sturdiness, and especially wheels. In either case you probably want the ability to mount wide tires (min. 35 cc) as suggested above, plus probably rack and fender mounts.

Really depends on what the trail is like: if it is a smooth dirt or gravel road with only pot holes, you might get by with a more hybrid-like bike, but if there are rocks, holes, and other obstacles, then you'll probably want a MTB. I've never felt I needed suspension myself.

Looks like a great ride to start the day with!