From: The Imperial Palace.
I attack on Turn 1. If I wait a turn after bombardment and airstrikes, that sometimes gives the enemy time to recover. I find it best to attack in the same turn I bombard.
Yes, I lead with infantry attacks. In fact, whenever possible, I attack with infantry. I treat my tanks as precious assets, because they are not so easily replaced. I use them to exploit and encircle.
I attack in weak spots all along the front, but not that many weak spots. I don't like attacking without arty support, and arty supply is limited. (I like the way the arty-supply rule indirectly forces one to prioritize and time one's offensive actions. I prefer a system like the OCS boardgame series, in which supply is on-map, but this computer game's arty rules are a decent approximation of that set of rules with much less complexity.)
In general, I try to avoid frontal assaults and to encircle the enemy, or at least to threaten encirclement. I try to cut roads and RRs. Until recently, I'd been liquidating pockets the turn after forming them, but now I'm waiting an extra turn.
I'm doing okay vs the "Normal" AI in the Case Blue scenario. It's August, and while I haven't taken Rostov, I've taken my initial objectives and asked for more time to get Rostov. My casualty ratio is better than 4:1 in my favor, which is roughly what I'm aiming for. I would think I'd be in big trouble if I were trading casualties one-for-one.
But I'm no expert, and I'll probably fail miserably in the end! Just trying to respond to your inquiry. :)