Joined: Mar 2014
Posts: 18,274
Likes: 6,632
From: ,location, location
Bikes: Foundry Chilkoot Ti W/Ultegra Di2, Salsa Timberjack Ti, Cinelli Mash Work RandoCross Fun Time Machine, 1x9 XT Parts Hybrid, Co-Motion Cascadia, Specialized Langster, Phil Wood Apple VeloXS Frame (w/DA 7400), R+M Supercharger2 Rohloff, Habanero Ti 26
So is the bike a brokie now?
As far as the entire project get something that has track ends or at least semi-horizontal dropouts if you are stuck on going fixed. Yes you could magic gear it and get a White Industries Eccentric Hub but honestly get a bike designed for being a fixed gear. Also a modern bike won't really look like a vintage bike with tapered carbon forks and modern aluminum tubing.
In terms of B.B. length that will be determined by your crank. Check with the crank manufacturer to see what they suggest or if it is something vintage check VeloBase or Sheldon Brown.
Me personally if I had to go with a square taper crank it would be the Sugino Super 75 which uses an ISO B.B. in 109mm or the Phil Wood Track Crank which is JIS 103mm. However I am quite happy now with my Sugino 75 Direct Drive because the outboard bottom brackets are a bit easier to work with..