EDIT: Ignore all this. I thought this was the BlackICE forum.
I haven't had any issues defeating Soviets (historical, veteran, all sliders +3 except me).
My army is usually infantry (two 60x infantry armies, conservative stance). 2 AT guns + whatever mountain troops that make 30 width. Support companies are HQ, maintenance, logistics, field hospital, engineer, armored car, medium artillery, heavy artillery, mountain support unit, commando. I set one big offensive line for both armies and hit execute. Replace a mountain unit for a tank when you have enough production.
I usually only have 2-4 armored divisions for my personal enjoyment, but the infantry do most of the work.
I spam fighters and the only micro I do is rearranging them when the front moves forward.
You need to repair infrastructure as you move forward. I can't emphasize this enough. Usually all of my factories are spent repairing infrastructure.
I have a garrison unit in every port and VP along the coast. For flavor, I use SS garrison units, 19-20 width total. Support companies are HQ, logistics, engineer, motorcycle recon, medium artillery, coastal artillery, support AT, support AA, police. 1 for each port/VP. I keep the event-spawned motorized infantry/armor divisions as a reserve.
Once you discover which ports the AI likes to naval invade, throw a couple more garrison units in those provinces.