I don't see distance as relevant.
The terrain, the rider and weight carried should have more bearing on the cog and chainwheel chosen than should the distance.
I respectfully recommend that new fixed gear riders acquire the tools to change their cog, chainwheel and chain, and that they experiment with different gearings in order to discover for themselves what works best for them in their situation.
When I first started riding fixed, I went up in gearing to 82 gear inches.
I have since gone way, way, way down to 61 gear inches and, not only do I get around pretty quick at 61 gear inches, I feel safer and have more fun.
Experiment.
Find out for yourself.
I recommend a separate chain for each cog and chainwheel combination.
Oh, and invest in a modest work stand for your bicycle: it makes it sooo much easier to work on your bike.