The 20" folders ride very well. I have taken 50 mile rides on my Dahon Jetstream. This is a fairly expensive better bike, probably not what you are looking for, with 24 gears (3 speed internal hub and 8 speed derailleur). But the principle is the same -- 20" gets you reasonable stability and normal speeds on flat ground; going fast downhill (over 40km/h or so) it becomes scary compared to a full sized bike.
But on flats, it's basically equal to a good full sized bike, so you can cover a lot of miles and thus a lot of ground, making the bike a really useful "land tender". If the terrain is not too hilly, 10 or 15 miles each way is just not a big deal, even for a middle aged old fort like me.
The 16" bikes are quite a bit easier to stow (I also have one of these), but they are really not much good for riding any distances.
You will certainly want to avoid single-speed bikes if you possibly can. Seven speed derailleur bikes are cheap
enough. My 16" bike is a 3 speed -- the internal hub is very convenient, but the gear
range is poor if you have any hills to climb. Unless you are really just literally going around the block, I would go with a 20" bike with at least 7 speeds.
A big PITA with bikes in general is that a decent lock already adds back as much weight as you've saved by buying
a good bike. I have a Kryptonite "Fuggedaboutit" which is like carrying around iron ingots. I'm thinking about one of those titanium locks.
A fold-up bike trailer would be great for hauling provisions.