I agree this is a great site for detailed info on Elgin.
As far as I understand (better Google it) going barrel is the usual configuration where you wind the mainspring via the arbor and the barrel drives the movement. there are other styles like motor barrel which is the reverse. you wind via the barrel and drive the movement with the arbor. This is safer for the delicate gears if the mainspring should break. Steel barrel should be obvious, most i’ve seen were brass. Thick or thin is a bit more tricky, should be dimension info somewhere.
Anyway glad it helped I use this site all the time.