All orders of battle merely give a snapshot of the army at one point in time: and the Russian Civil War even more so than most wars. What lists we have tend to be associated with a reorganisation, so are much better evidence for the months following than for the months preceding them.
Note: different armies counted differently. The Whites tended to count only actual riflemen as "bayonets" and just line cavalry as "sabres", so not including any supporting troops like machine-gunners. The Reds tended to count everyone in a rifle unit as a "bayonet", whether they served a weapon or not. The Reds also tended to have more non-combatants in a front-line unit than their opponents. It is therefore inappropriate to just compare the straight figures directly.
Some early war lists, showing the typical mix of units for the time.
The forces facing Kolchak, the Orenburg Cossacks and Urals Cossacks in the middle of 1919.
The forces in Fergana, largely garrisons and fighting the emerging Basmachis. This was just before the collapse of Kolchak's forces, so was still the isolated forces of the region.
An orbat for those elements of the Soviet Southern Front at the crucial turning point of Denikin's drive on Moscow. Known as the Battle of Orel or, in Soviet literature, as the Orel-Kromy Operation:
The forces across the Don and Manych, February 1920
The 1920 Polish War, from Гражданская Война В России: Война С Белополяками (Civil War in Russia: War with the White Poles) by Kakurin and Melikov.
An orbat for those units facing the White "Russian Army" in the Crimea above:
A bit of a resource for tracking down Soviet Cavalry divisions: especially useful for when they changed names.
A resource listing all the major units of the Red Army composed mainly of foreigners.
The "Internationalist" units that lasted to the end of the war, with numbers.
The Trans-Dnepr Operation by Tom Hillman has good orbats in the back relating to the forces involved.
The Role of M.N. Tukhachevskii in the Suppression of the Kronstadt Rebellion by Neil Croll in Revolutionary Russia, Vol 17, No. 2, Dec 2004 is easily the best source of unit information on the Soviet side that I have seen.