I’m building up a fixed gear on a 1970s Claude Butler frame. Never done it before, lots to learn etc.

I’ve got a Miche Primato 165mm chainset, but what bottom bracket do I need? The Primato BB widths seem to range from 107mm to 119mm. Amongst other things (eg. compatibility), I want to be sure of chainline... the rear hub will be a Sturmey Archer S3X 3 speed fixed hub, 120mm. I checked with uncle Sheldon and he says stuff about halving the OLD and subtracting the dropout-to-sproket distance, but I’m still not sure where this leaves me with making a decision on a bottom bracket. Halp!