That's just how CoH is! Perfectly normal. You just have to figure out the timings and counters, but it takes a while before you start to get the hang of it. And when you think you got it, you'll get rolled by something completely different.
To get a feel for the soviets, I'd start by playing with conscripts a lot. You can basically make it through an entire game with only conscripts and AT-guns. The conscripts can do anything if they get the upgrades for it. Normally you want to keep the pressure on the germans (attack, harass and capture) and get a small advantage going into the mid-game. Conscripts are stronger than Grenadiers in close-range.
German T1 gives the player a lot of choices for support-weapons as well as the core infantry (Grenadiers). Try bulding 4-5 grenadiers and perhaps an mg or two. This should be enough for you to keep some territory before you commit to any tech. The germans can't spread out as much, they need to stay closer together so they wont get outnumbered by a soviet flank.
In general you could say that an army should consist of 4-5 infantry squads, 1-2 support squads, 1-2 AT-guns and then finally tanks. Also I find it that playing against AI really put a strain on your micro since they really like to spread out and fight all over the map rather than making coordinated attacks.
Excellent, that's what I'm looking for. Seems like I'm trying to "tier up" too soon. But it seems with the CPU...that they have a distinct resource advantage (EVEN AT STANDARD!)...so that's why I'm having so much trouble with counters. Tanks start rolling out before I have anything to counter with, and I can't tell to either go with infantry upgrades for AT...or just to go with AT units.
I'll try to post a replay...but can you post Vs. AI replays?