To Bike Forums, Eugene_B!
We will try to answer all of your questions to the best of our abilities!
You've given us excellent information from which I'm most certain we can recommend several bicycle types that can best suit your needs.
From the excellent photos that you've provided, I would suggest that you select from one of three categories. Those of which will be cyclocross road bikes, hardtail mountain bikes, or special touring bicycles. Actually, most any type of bicycle that can be equipped with wide tires, has eyelets for a rack, and quite possibly fenders.
Would you prefer fenders to protect your clothing from splashed puddles, or not?
Would you prefer drop handlebars or flat handlebars?
Drop handlebars are curved and when riding "in-the-drops", you assume a more aggressive and greater aerodynamic riding position.
With flatbars, you sit more upright, and while riding "on-the-hoods", you're better able to see traffic.
If you are in anyway mechanically inclined or live near a bicycle co-op, my first recommendation would be the Surly Truker Deluxe frame. You can build the bicycle up with your very own components independently, if you're mechanically inclined, or with the assistance of your local bicycle co-op, if you're not so inclined.
http://surlybikes.com/bikes/trucker_deluxe
Of course, you could always just have your favorite LBS build it for you at the going local rate.
At any rate, when complete, the bicycle will have wide treaded tires, a rack, and possibly even fenders, if you so desire. If you like, you can pattern its build after Surly's 26" Long Haul Trucker so that it will look something like this:
http://surlybikes.com/bikes/long_haul_trucker
Or you can vary the components loosely along those lines.
The Surly Trucker Deluxe has SS couplings which can be loosened and detached. This allows you to deconstruct the bicycle so that you can disassemble it for the purposes of either easy transport, or security against theft.
IMO, a folder would be only a mediocre choice given your terrain and desire to traverse long distances.