It depends on what army you were fighting with and which units you were apart from. More elite units like an SS unit or Panzergrenadier unit were given the best gear and weapons. Other times like in Stalingrad whole squads of Soviets were issued SMGs for CQB. But usually the units of a basic squad was the following.

The standard German squad consists of 10 men with 1 MG/34-42 gunner, 1 MP-40 SMG, and 8 Kar98k bolt action rifles. A Russian rifle squad was 10 men and consisted of 2 SMG, 1 DP-27 LMG and 7 Mosin Nagat riflemen. However as the war dragged on the squad could consist of 1-7 more SMGs. A US rifle squad of 12 men would have would usually consist of a BAR LMG, 1-2 Thompson SMGs and 10-11 M1 Garands or M1 Carbines. However take these numbers with a grain of salt as US squads could get more Thompson’s from Company HQ for a mission, also some Soviet units were completely equipped with SMGs and light machine guns at times.

Usually the NCO was issued an automatic weapon alongside the Light machine gunner. However his loader or carrier of extra ammunition for the LMG was usually issued a rifle or in some cases just a pistol. But to answer you question; if you were an average German soldier you were usually stuck with a bolt action rifle, Unless the MG died and you had to take over or you were NCO you didn’t have an automatic weapon. If you were an American soldier you could have gotten a Thompson if the mission required it, but you had a semi automatic M1 Garand or Carbine which was better than your German counterpart most of the time. If you were a Soviet you would be issued a bolt action rifle as well early in the war, but by the end of the war you had a better chance of getting an SMG.