I would say successful means issued in some numbers as a standard troop weapon. I would have guessed the M1 rifle, but that seemed too easy. Thought there may have been something before that, even if it had a limited service life. I could not think of anything from the russians, germans, brits or french. So maybe the first was indeed the fabled Garrand.
The Thompson might be correct though I was thinking more of the standard troop rifle.
Of course, archy would know the nuts and bolts.