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You're welcome: BB are a nightmare.
103mm is quite narrow and I can't think of any track cranks that use that off hand: perhaps ask the previous owner what they used.
Ominous are a safe bet: if you do buy second-hand, budget for a new BB: the original has a patchy reputation, whereas the new, redesigned version is fine.
Search for "SRAM Omnium" on here: there are a couple threads covering things like BB and clearance.
Thanks a lot for your comprehensive post @Scilly.Suffolk, it really helped!
Yes, that is the internal bottom bracket I seem to have on the frame according to their specifications.
Bit overwhelming for me but I got the basics and I think I'd go with the Omniums. I am a total beginner and this is my first build, having bought the frame already. I am pretty sure I will have many more stupid questions regarding one thing or another :).