The most issued weapon in the war was still the bolt action rifle.
In the American military, it was the M1 rifle.
American Army.
We operated on a TO&E or Table of Organization & Equipment.
This was an official plan of who was to get what. Riflemen got rifles, machine gunners got pistols, SMG's, or Carbines, Officers and Sgts got pistols and Carbines, etc.
After the TO&E was met, it was sort of "first come, first served". Of course, officers usually got what they wanted.
Almost everybody wanted a SMG, and SMG's were kind of "community property". If a patrol was going out, it was expected that SMGs would be loaned to patrol members.
If you were a casualty, your SMG stayed with the unit.
British Army.
Passed out STEN guns and Thompson's heavily to Commandos and lots of other troops early in the war, and lots of STENs throughout out due to the speed and low cost to make them compared to a rifle.
Later in the war, the big users of SMGs were the Commandos and paratroopers.
I'm not sure, but I got the feeling that he Brits didn't use SMGs as heavily as we did, later in the war.
Germans.
Hitler liked the SMG concept, and the Germans used them heavily, especially on the Eastern Front. Usually officers and Sergent's got first pick, then the regular troops. The SS got first pick also, and were probably the biggest users.
Russians.
Were the heaviest users of SMGs in history. Entire battalions were armed with SMGs and nothing else.
The SMG was cheap, fast, and easier to make than a rifle. It required little training, and the Russians passed them out in huge numbers.
In all army's, SMG's usually wound up in the hands of officers and Sergent's who had the "pull" to get one if they wanted it, and elite troops like paratroopers, Rangers, and Commandos.
Ordinary troops usually got a rifle, until they too got enough pull to acquire one.
In the Red Army they were passed out like hotcakes to anybody and everybody.