One big problem I can see if you try to stick to the books with the US organization, is that battalions are specialized.
In other words, if you buy only these three companies that one actual Lt.Col. is supposed to command according to TOE, you would end up with 1)three identical infantry cos, 2)three identical tank squadrons, 3)three identical whatever without much variety even in the supporting units.
That's also not counting the cross-attached support units from division level (arty, air defense...). As far as I've understood the old FMs, the tank and mech battalions within an armored/mechanized division were rarely used as such and mainly mixed and matched as battalion-sized task forces.
In my opinion that'd be the way to go to be as realistic as possible (and that's important) with regard to the books
as well as actual field practice. Since you're at GlobalSecurity, you can try
FM 7-20 about infantry battalion command, they should have something to tell about cross-attached support and task forces.
To get a balanced force, I'd advise sticking to only 2 of your core unit type (say infantry), one company-size group of another branch (say armor), and three to six platoon-size support units (arty, recon, AAD, engineers).
Or you can always get a balanced battalion-sized US force by buying you a heavy Cavalry squadron, but not if you want to be original!
