Few points -
I never tried, but don't like the idea of fixed gear in traffic. Scares the sh%t outta me in fact! That's why I suggested a BMX freewhell rig.
Tires - I used to ride the skinniest $20 Continental tires I could get, like 18mm. These did me fine up and down curbs, and the occasional flight of stairs. Pumped up to 100PSI they were zippy. Just replace them often.
None of these fat ass 2.whatever "hybrid tires." Oh yeah, slicks work in the rain at that size too. More rubber on the road.
My bike was a cheap ass TREK road bike. I put straight bars on it, and MTB levers. Then I had a wheel built for the BMX freewheel, and clippless pedals. That was one of my favourite bikes ever. It later raod from here to Halifax (with gears again).