Buy a bicycle. You want a hard-tailed mountain bicycle (that's the one with the moderately fat tires -- not the really fat tires, but tires that are slightly fatter than the average bicycle). "Hard-tail" means it has no suspension in the back. Start riding it every day for at least an hour. In a few months you will have put yourself into shape, and you will possess a mode of transportation that can carry you and a hundred pounds of freight over any terrain known to man. And the best part is, it runs on canned beans. When the crazy time comes, and the gas stations no longer get deliveries of gasoline, you will understand how smart you were to get a bicycle.
Any terrain is a big stretch. If you're going to be doing offroad/offtrail at all, consider the fat tires. I'm currently running the fattest tires I've ever run on my xc bike. Even unencumbered you're not making any type of progress through sand or snow, even on 2.5s. You can air up the fat tires if you want to ride on trails or roads, and you can air down to almost flat especially with runflat inserts.
That being said, if you're in the hills, sand, snow etc you're probably better off to just walk the bike. Even on moderate terrain with 100 pounds you're much more likely to break and wear parts, wipe out, or just exhaust yourself trying to ride up hills.
I don't own a fat tire bike, I just don't find them as fun and I walk my bike when I run into deep soft sand, but they would be what I recommend for a bug out bike.
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