I am about to have a b.b. and crank put on my Surly Cross Check, and have found a crank I like which is the Stronglight Ironlight https://xxcycle.com/ironlight-titane,,en.php , but need to know what specs I need to adhere to while selecting a b.b. Particularly, I need to know what this crank's interface is; ISIS, square taper, etc. Regarding threading, I think the Ironlight uses British.
Spindle length is also a question for me. One b.b. I saw has a selection of either 108, 113mm or 118mm.
The Cross Check's b.b. specs are: 68mm wide, standard English threaded 1.37" x 24t
Right now, I'm looking at the Hope Stainless Steel for a b.b.

Paul

the Ironlight definitely has a square taper spindle interface and, as a bonus, includes self-extracting bolts. The one reference I found thought it was JIS but wasn't certain. I recommend you contact the seller for the exact configuration.

Your Cross Check is English threaded, 68 mm bottom bracket shell as you determined and the above reference said a 110 mm spindle length so the 113 won't be too far off.

I have a couple Stronglite cranks , JIS Square taper..

I have had the Self extractor just push the threads out of the crank arm,
rather than budge the crank-arm, so not always a 'Bonus' ..