Cheap folders are an exercise in frustration.

It's difficult enough to design and spec a non-folding bike in a size to fit you and keep it relatively inexpensive. Add the complexity of a folding mechanism, and what typically happens is that most of the $ go into the frame and leaves almost nothing for components and wheels, meaning you get the bottom-of-the-barrel parts spec and a pretty heavy bike. Not exactly conducive to riding, folding and owning one. Lots of people give up entirely on folders at this price point, which is a shame.

On a cheap folder, the parts are usually heavy (stamped steel in some cases) and don't work well and/or go out of adjustment easily. So then the frustrations begin: folding hinges that have all kinds of play with minimal use, squeaks and rattles galore, derailleurs that protest shifting or stop shifting entirely, brakes needing constant adjustment, wheels that go out of true at the drop of a hat....you name it.

Before you drop a couple hundred into a folder that fits the above category, see if there's a small non-folding bike that might work for you at that price point. Used, you could probably find a Trek, Giant or Specialized hybrid in 15" size that wouldn't be terribly difficult to tote around. I refurb bikes, and my bread-and-butter is completely refurb'd bikes that I sell in the $150-200 range.

Increase the budget past $200 and you start getting better options in a folder. But unless you're willing to put up with the problems of cheap folders - like doing all the maintenance yourself, because folders tend to require more maintenance than non-folders, best to stay away from cheap folders for the time being.