Thompsons were usually issued to officers, but anyone who could scrounge one up could uses one. There were never really enough of them made, and the early ones were expensive to make ($200 apiece for the 1928 version). The M1 and M1A1 versions were cheaper, but it was still an expensive and heavy gun, so it was phased out in favor of the "grease gun" which, while reliable and practical -- and cheap -- was not so well liked.
Thompsons were close in guns, very good in street to street fighting and other types of close contact situations, but not accurate or far-shooting enough for longer range work.
The M-1 Carbine was originally intended as a replacement for handguns since it was easier to train soldiers with, and really for what's considered "rear echelon."
That being said, it did find its way to the lines and was liked for its lightness by many, and criticized by many who treated it like a rifle (like the Garand) because it did not have the punch of the .30-'06.
At the outbreak of the war bolt action rifles would have been the most common infantry arm, but as the garand entered service it very quickly became probably the most common; atleast among all the photos and movies of WW2 most soldiers are carrying Garands.
Although limited to 8 rounds it was pretty easy to reload, and packed a wallop that neither the Thompson could (save for the effect of full auto) or the Carbine. It was effective both close in and at long range.
I think it was usual for there to be one Thompson gunner per squad ... but having said that, it's possible some squad might not have had one, or other might have had two.
If you can locate the book, US Infantry Weapons in Combat: Personal Experiences From World War II and Korea by Mark G. Goodwin Published by Scott A. Duff Publications (2005)
P. O. B. 414
Export PA 15632
you can read some experiences real soldiers had with their weapons, from the Garand, the Thompson, the Carbine, and others. It's pretty interesting.
