You really need horizontal dropouts to tension the chain. You can get chain tensioners, but that defeats the simplicity of a singlespeed.
A single chainring crank can be used with a narrower BB spindle, to give a much narrower "Q-factor" (pedal to pedal width). Use a thick ring with no cutouts or ramps, and match it to a thick chain.

Look for a "flip-flop" hub, fixed on one side, frewheel on the other. Goldtec make a really nice singlespeed hub.