Where do you live? You want to go try some bikes. As a height challenged person, I actually find the 20" wheels a LOT more enjoyable for riding. They accelerate faster, it's way easier to stop and put a foot down, and they are more nimble for city riding. A 20" folder will also occupy a lot less space than a 26". Do you have any dealers nearby? In your price range, it will either be a used bike or maybe a basic Dahon or Citizen Tokyo. Not sure if Downtube has a model in that price range. Do you have stairs to your apartment so you'd have to carry the bike? Then weight might be a factor.
Folding bikes will ride as far as any other bike - assuming it fits you well enough. As a new rider, you want to avoid department store bikes or anything that is made so badly you won't enjoy riding it. Will you be riding flats or hills? That will also impact what you get. If you shop around, you can get a Dahon Boardwalk (single speed) new for around $200. Citizen Tokyo has some multi-speed bikes around that price range. You can get a Downtube for around $250 with multiple speeds. You need to find a place to try some bikes first, though.