A, maybe B
Extrapolating from your earlier post about your nation having multiple areas of conflict, I would guess the best deployment would be one regiment in each division being fully mechanized. This gives each "region" organic mechanized support without having to request deployment from higher commands. Generally speaking it's better to have elements deployed as far down the chain as possible while still maintaining the necessary cohesive "punch" of whatever you're distributing. In this case one company per battalion is probably insufficient "weight" because each company would be too small a force to be decisive on its own, and would need to be pooled with other battalion's mech companies. The possible exception would be in your "Desert" zone where it's mostly anti-insurgency work. The other problem with company-sized deployments is that they'd be tied to the slower speed of the other 3 infantry companies once the air transport departed, negating a good part of the benefits of being mechanized at all!
That being said, a Mechanized division has its advantages logistically, especially during peacetime. In wartime if they're trained and equipped to operate mainly at the regimental level the division (barring the largest operations) would likely cease to exist as a unit except on paper. Instead its regiments, which had been kept together for ease of logistics and training, would be seconded to the other 3 non-mechanized divisions. The modern US Army functions like this quite a lot, with divisions being more paper/peacetime formations, and brigades/individual units within those divisions being sent hither and yon on their various deployments. If your army is professional enough to operate in such a manner a mech division would serve you well, because if you need to concentrate more than a regiment's worth of mech you're not fighting with individual divisions for it. Much easier for army politics to re-assign a seconded unit to a different command than an organic one!
TL/DR: Option A is the easiest to implement while still getting the job done. Option B is viable if you have excellent internal cohesion and training.