What to look for when buying a single gear bike?
Some other items you might consider:


Most importantly, the fit of the bike. If you are 6'2, you will be on the high end of normal sizing, and not all models may be available in a suitable size. Staff at any decent bike shop should be able to measure you, and suggest a range of suitable models however. Take them for test rides and make sure you don't experience knee pain or back pain. 
Weight of the bike. If you will ever have to carry the bike, this can be quite important. For example, if you live in a flat above ground level, and don't want to leave your nice new bike outside at night where thieves can get it. Single speed bikes tend to be lighter anyhow, so you should have no trouble finding a cheap model that's still under twenty pounds.
Low maintenance design. If you want a low maintenance bike, single speeds are a great start. I'd also look for a coaster brake (back-pedal brake), and a nice chain case, possibly even a full chain case if you can bear the weight. An aluminium frame may also be a plus, as ChroMo (Steel) will rust relatively quickly without careful maintenance in wet climates, especially if there will be salt on the roads in winter. 
Fenders if you ever plan to ride in rain, mud, or snow.
Rack Mounts if you ever plan to carry something heavier than a backpack. Also useful for riding in the heat.