It may seem like an odd way to play, but I generally build a lot less armor than most players: typically one Corps of 3-5 Armor and Motorized divisions per Army with 3-4 Corps of 5 Infantry divisions. That's generally around 1-2 ARM divisions, and 1-3 LARM or MOT per Army, and perhaps 8-16 ARM and LARM divisions total for a country like GER. Basically, supply on the Eastern Front is rarely a problem. Many of my most successful encirclements have been almost entirely with Infantry, while the bulk of my Armor was busy elsewhere, or were done with smaller countries that can't even build ARM except via Licensing.
The AI is pretty decent at pulling back units that are in danger of being cut off, so you have to push deeper and take a bigger bite, otherwise the fleeing units will hold the gap open as you fight and break each one in turn, until you're left with an empty pocket (and Manpower pool). That's generally more provinces on the perimeter to hold than I have armor or motorized units, which may (or may not) form the spearhead, but the rest of my pockets' walls will be held by INF. Forget pocketing a division or three, go for 12-20 at a shot, and be prepared to hold that perimeter against simultaneous attacks from both inside and out.
Multiplayer is a different animal, and you have to "min/max" and game the system to compete against the players who are doing exactly that.
As for "instead of AT", I don't put AT in every division, only enough to deal with opposing armor as needed. AT has close to the worst Soft Attack in the game (MPs are worse, and ENG are comparably bad), so it's ONLY useful if you're fighting against tanks. Even then, aside from the Piercing stat, most of the opposing Armor divisions consist of one hard brigade and several softer ones, and your AT is weak against MOST of that Armor division. Another INF or ART might make more sense in most cases, with one or two AT divisions per Corps for when you actually need them. The AI armies are often weak BECAUSE they use so much AT. The main purpose of ARM, in my opinion, is to force the opponent to spend IC, Manpower, and valuable brigade slots on AT, to counter it.