People have done long distances on many different folding bikes but the most popular are Brompton (quick and efficient fold) and Bike Friday (not as convenient a fold as a Brompton but more akin to a
Rivendell than a Brompton as far as ride quality is concerned). However either of these will run you upwards of $1300 so what is your price range? I see that you spec'd "Walmart specials" as your bikes so you may be looking for something more "entry level".
If your price-range is less than $600, my advice is to go with a steel frame as opposed to an aluminum (properly "aluminium" if the masses are correct) one because although alu frames are usually lighter, in the realm of low-cost frames that low-price bias means that the hinge design is probably lacking which is a major point of weakness in a "fold-in-half" frame design.
So in order to offer any relevent advice I'd have to ask... what is your price range?