Is the smaller ring on the front of the Varsity a 39t ? That should work pretty well, and it won't be 'ramped' so should work well for a single speed. You won't have the leverage one does from a standard bicycle configuration, and yes, hills will be an issue. The small wheels in the back won't provide much momentum or 'carry' once you get it up to speed.
I'd say maybe a 21 or 22 t rear cog. And that still might be too much.
I'd say maybe a 21 or 22 t rear cog. And that still might be too much.