How to know what size bottom bracket to buy
More than likely it's a 68mm wide English threaded BB shell on the frame. You may just want to wait until you get the frame to verify that. The Tech Specs on page for the crankset actually do say that it's designed for "103mm bottom bracket" and "JIS Square Taper". Those should be all the measurements you need (assuming the frame is 68mm English): 68/103/JIS.

If you want a matching Sugino BB, here's one: https://www.ebay.com/b/Sugino-Square-Taper-JIS-Bicycle-Bottom-Brackets/177805/bn_5810397