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@Rincewind
great, some detail. I will save you some extra research time.
yes, you want a quill stem for that frame and headset.
Crank length depends on rider leg length. longer legs get longer cranks, longer cranks have more leverage, shorter spin easier. longer legs reccommended longer cranks, shorter - shorter cranks. If you are the right size for that frame I'd suggest 165mm. If you want a classic look get silver square taper cranks, SR and campy pista show up on ebay often.
track BB is usually 107mm for good chainline.
The frame probably isnt 700c, a front brake may not fit very well, you'll need long drop.
As said seatpost is 27.2, standard for most, especially english reynolds tubing.
rear spacing is 125. standard track is 120, use washers to get correct size.