dabac

A 27" wheel will get you away from the issue of brake reach, so that's good. A wheel built around a 130 mm freewheel hub is a tad weaker than a track/flip flop wheel but should do just fine. Might need some dishing or spacer rearranging for chainline adjustment.
Your frame probably has a 126 mm rear dropout width, but, being steel can easily be cold set or simply ignored. With nutted axles you're not looking at lightning-fast wheel changes anyhow.
52/16 is a fairly steep ratio, I certainly wouldn't want to ride that as a daily beater, particularly not when lugging things around.

Also, looking at the pic, I'm intrigued by the saddle vs bar height. You certainly don't find many bikes set up like that. The saddle is also scooted way forward. Are you sure this frame fits you?