My post will be written from a 1v1 perspective.
I find a core base of 4 infantry squads - 4 grens or 3 Grens and a PG, 1-2 Machineguns, and a Pak 40 to be a good core.
Depending on the situation, getting a mortar or a sniper in addition to the above list works well.
As was mentioned previously, two Stug III Gs are effective at shutting down enemy armor. Mines help considerably, especially on maps with choke points (Kholodny Ferma) or lots of roads (Langreskaya). If I get two Stugs for AT, a command P4 is definitely a good option.
It modifies damage in the aura to the value of 0.8, effectively giving all your units 20% more HP. With the P4 command tank, my preferred commander would be Blitzkrieg; Panzer Tactician improves survivability of armor and Stuka CAS can be game-changing late game (I usually get 2 muni caches to spam the damn thing).
Typically, instead of 2 Stugs, I will go for P4s. One, usually two. With Lightning War, it's possible to get 2 P4s and a Tiger - a fearsome AT and AI combination, especially when the P4s get to double vet (increased armor, HP). At that stage I usually just tech up to T4 and replace any P4 lost with a Panther. This assumes that I keep my vetted LMG grens alive, partially fulfilling the gap of AI if I lose a P4 and replace it with a Panther. NB: with Lightning, you also get access to Stuka CAS
Vehicles I recommend ignoring would be the Brummbar. a Panzerwerfer can just be a waste of fuel and popcap in 1v1 when you need a panther or you need a P4.
Mobile Defence doctrine is definitely viable. Command P4 w/ double Pumas (who have Target Weak Point, just like Stug) can effectively keep medium armor at bay. You must tech up against Jacksons or heavy soviet armor, unless if you manage to lure said vehicles into a teller in front of a couple Paks/schreck Pgrens.
But, really, that base I put up there, that's where I like to start. After that it's all up to you.
It's certainly viable to get a 3rd MG anytime in the game. But remember, always keep your MGs supported with a unit ready to cover their flank or scout for maximum-range suppression.