As for armor, I used LARM for quite a while, but now tend more towards ARM and HARM usage.
An early combined arms all-around armor brigade consists of ARM/ARM/MOT, later I swap in SP-ART (ARM/ARM/SP-ART) and even later: MECH (ARM/ARM/MECH/MECH).
Another setup I use is ARM/ARM/ENG/ENG. While this division lacks firepower, it has great all-terrain abilities on attack and defence and is even able to attack sucessfully over rivers, something that can really ruin your opponent's day in MP.
HARM/HARM/HARM/HARM are heavy breakthrough and anti-armor divisions, but I usually have no more than 2-4 of these around. At rare occasions I also use them as heavy defence forces for strategic points, for example Gibraltar, Malta and alike. Any seaborne assault against them practically futile, so as long as I can keep my supply lines intact, the enemy won't get an island where these beasts are located. Sometimes I use smaller stacks of HARM/HARM, mostly for beach defence or when a frontline is too large to cover by a single HARM division.
LARM/LARM/AC/AC or LARM/LARM/MECH/MECH are nice fast divisions, although LARM/AC definitelylacks too much firepower for my taste.
However, the thing I REALLY like is the MOT/TD combo. It is incredible cheap to build and support, fast enough, gives practical for MECH and provides adequate combat stats with low research investment.
I usually use MOT/TD as reserve and support units (for example for securing France). MOT/MOT/TD/TD is a great armor substitution - and with advanced techs (iirc LARM 1940), you can even use MOT/MOT/TD divisions with CA bonus.
As Emu said: MOT/TD is a GREAT (if not exploitive) combination!