I actually rarely use the in-game battle plan function. I know this gives you a combat malus but I found that the spearhead plan behavior is too stupid to tolerate.
Planning bonus decays 8x faster with right click orders. You can instead repeatedly make new spearhead orders (even on 1 province distance) and execute them when you really need the extra modifiers.
Generally a straight line spearhead from units created for dedicated attack mostly works. Chained spearhead orders bug out horribly and will often send units careening far beyond the green-highlighted path, sometimes even in an opposite direction. So stick with one spearhead and cancel/renew once units get to destination. Also worth manually micromanaging units behind the spearhead, because if you don't the AI for it is bad and you can and will be counter-encircled.
Even with all those considerations, having 30-60% more of everything from soft attack to breakthrough is strong enough to merit learning to use it. If you're in a dominant position with experienced + high damage units you can skip though.
So what I do is, I make small armies of purely armored divisions, each one supported by an ideally-larger army of motorized infantry (I don't even really bother researching mechanized as imo the bonuses are not really worth the disruption in production you get from switching from trucks to halftracks).
Researching mechanized 1 gives you bonuses to your motorized even if you don't switch, so you should generally research mechanized 1.
Actually building/using mechanized equipment is generally not recommended, however. That IC is better spent on tanks or planes.
Keeping tanks on tank commanders and infantry with their own commanders is good play. Commanders get traits that benefit a unit type, so you want to maximize your benefits.
Standard infantry division composition is 7 infantry battalions and 2 artillery battalions with engineering, logistics and artillery support companies, and I usually add an anti-tank company later on.
FYI this stopped being meta a few patches back. Artillery got nerfed, so 7/2 is only marginally better at damaging than 10-0 infantry with a support artillery. The latter costs significantly less IC to produce and actually holds up to powerful attackers a little better. In a direct fight between 10-0 and 7/2, the attacker will lose pretty badly regardless, so I recommend the cheaper option. These are mostly made to block/hold line rather than attack unless you're very advanced with micromanagement/pinning attacks and planning bonus/leader trait manipulation.
Yikes, had no idea support companies decreased organization. Will have to look at the statistical effects of each one in-game next time I play.
TL DR version is that the division designer has a weird algorithm that mixes a "stat of the highest" with an averaging function for some stats. So putting a single tank can increase your armor substantially. This also means that you can lose piercing by adding support companies other than AA/AT, but the benefit they confer can be worth it.
I'd value having 5 support companies more than an additional tank if we're talking 16/4 vs 15/5 tank setups, as things like engineering, recon, and logistics are straight up more valuable to me than the marginal difference of a tank vs mot in a battalion slot.
Maintenance is only worth considering on low reliability designs or equipment capture memes with terrible nations (like playing as Chad or something w/o nation ruining allies otherwise). Support arty is still excellent value, 5th slot can be preference like rocket arty or AA. Probably not AT on tank divisions, you'll have enough in SP with just the tanks.
The most crucial thing in the game remains, in my opinion, the ability to either secure air superiority over the battlefield for yourself or to deny it to the enemy. Without air superiority, you will find it significantly more difficult to push. How you design your divisions does matter, especially in terms of connecting it to your chosen doctrine, research, and industrial capacity, but control of the air is a much less marginal advantage.
Yeah. Operating in red air is miserable. Even more so if the enemy uses CAS too, since CAS completely ignores division armor/defense stats and will tend to gut high expense, low-hp divisions like tanks. Worst case at least add support AA + line AA to offset the enemy air superiority advantage and shoot down/interrupt the CAS. This is still an enemy win because your division is somewhat weaker in ground combat, but at least you're not getting completely fleeced for -30% defense/breakthrough (sometimes more depending on enemy doctrine) in addition to attack penalties + constant shredding from armor-bypassing air damage.
There's also some weird interactions because this is a paradox game. For example if you use an odd spread of cavalry + infantry you can simultaneously train both cavalry and infantry leader traits. You can then add ~3 tanks to this division and it will still count as a "cavalry" division at 40w, which is also technically an "infantry" division. So you can get stupidity like + 100% division attack/breakthrough from commander skill, or maybe ~90% after the nerf. Combined with planning bonus, doctrine, and at least regular xp you can get a lot of power off of divisions that cost relatively little IC.