It would depend on whenever the soldier was in infantry, sailor, tankist, or airforces? Also by timeframe in the war. I would post what they may have worn in the beginning of the WW2.

If by average you mean an infantryman, then let's start from the top. Newer helmets were issued in 1936, before the war. The problem was that there weren't enough of those to go around. So, even into 1941 or so people were still using the older style helmet. Newer were from the photo SSH-39 and SSH-40 (#1 and #2). While in the beginning most used SSH-36 (#3 and 7), which was from what I recall looked almost identical to the ones used by French. Soldiers wore different types of rucksacks. Some had (and it was least popular one) leather rucksacks, the most popular among average infantry men would have been the one made out of (looking up the English word) "sailcloth". It was around 30 cm by 10 cm, and in height was around 28 to 30 cm.

This rucksack had two outer pockets, usually one contained accessories for rifles, while the other had personal hygiene products. Inside soldiers usually had number of foot cloths, and personal tent. Those who may have fought longer would have carried wooden pegs attached to the underside of the rucksack, so setting up the tent would be easier without having to hunt around for proper sticks and such.

The rucksack itself would have had a type of hooks, where more things may have been attached to. For example a bag with products may have been attached most probably underneath the main bag and slightly below it. Such "foodbags" would have had "dry" food, mess kit, and an aluminum pot.

Each soldier of Red Army was issued a gas mask and a bag for it. Most though threw the gas masks aways and used those gas masks bags as rucksacks.

Standard for an infantryman was to have two leather bags for ammunition. Each bag should have had four clips with than issued Mosin. Those bags soldiers wore on their belts, left and right sides of the belts.

Again most soldiers should have been issued a so called "grenade bag", such bags would have held two grenades with "pegs". In most cases soldiers did not have those though. If those were not issued and ammo bags were also not in stock, then soldier would have carried all that in any other bag he may have got his hands on.

Some soldiers were issued sapper shovels, they would have been issued in a cloth made case. Those would have been worn on their right thigh, just underneath the metal flask.

If the weather was bad the soldier may have worn a "cape" (plash-palatka). It was made from sailcloth and was greenish color. It had a braid of sorts which allowed it to be attached around soldier's shoulders. What is cool is that those capes could have been attached to each other, making it possible for more people to hide/sleep underneath them. (They were still popular in 80s and 90s as a part of a camping gear). Those "capes" were usually wrapped around "U" shape around their main rucksacks. Those who did not have rucksacks would have worn it wrapped around their chest, think like a bandolier.

Uniform and some items were updated in 1943, if you are interested I'll post more. :)

Sources:

Uniform of Red Army 1918-1945 by A. Shalito, I. Savchenko, et. al.

Red Army by Shunkov