Fit really comfortable tires. Biggest that will work well on your frame. I like René Herse/Compass. Tubulars work too. Inflate lower than normal. Latex inner tubes are worth it. You are going to get to know your saddle real well. I have fewer saddle problems than anyone I know, long distance fixed will test you and your saddle.
Picking a gear is hard. Plenty of reasons to go up a little and plenty of reasons to go down a little. I would go down a little and not worry about how finish time compares to your geared bike times.