dddd

Too big is too big, but there are three important caveats here, because this is a VARSITY.

First:
Varsity and Continemtal frames have very high bottom bracket heights to accomodate very wide pedals and the riding skills of beginners, so the possibility of using smaller wheels is worth considering.

Second:
The Varsity's frame size is measured to the top of the extended seat tube, but the Varsity's top tube is about an inch lower.

Third:
The frame geometry (specifically the layed-back seat tube angle) makes the top tube feel a lot shorter than it is, since it's entire length is moved rearward relative to the bottom bracket. And further, the layed back head tube angle means that a longer stem will mess up the bike's handling. These issues mean that a relatively tall frame is the best size when selecting a Varsity or Continental, particularly when it's a singlespeed where the rider occasionally needs to stand up and get their weight foreward to charge up steep hills or to accelerate from a stop.

Brianinc-ville posted a link showing that the small ring can serve as a single ring, with the heavy big ring removed.
I would consider this as the stock bb and crankset is very durable, creak-free, long-lasting and easy to service.
This is a Schwinn, not a Huffy, so these parts are actually made to very high durability standards, including Schwinn's finer 28tpi threading.