There were four options under consideration (in the order of preference):
a full-suspension alloy mountain bike, which to many may sound like a crazy idea, but there was rationale behind it (see my post Choosing the right bike on the Expedition Greenthorn blog);
a relatively lightweight (not overbuilt expedition type) steel hardtail mountain bicycle with standard MTB 26-inch wheels, a suspension fork (preferably, coil spring) and mechanical disk brakes;
a steel hardtail 29er mountain bike with a suspension fork (preferably, coil spring) and mechanical disk brakes;
my old aluminum hardtail bike with a coil-spring "air-assist" (I think they don't make those anymore) suspension fork and rim brakes.
I decided to go with the third option: a steel hardtail 29er (see my blog post Got the bike on the Expedition Greenthorn blog for more info).