You want the 1959-1962 manual series designed for the ROCID/ROTAD organizations. The squad/platoon/company/battle groups have different TO&Es than the post-'63 ROAD units.
This is a Google Drive folder with FMs and some issues of Infantry magazine from the period.
This includes:
-Ordnance Corps stock and data on all items they handle circa 1961
-Australian Pentropic organization
-Infantry, Artillery, and support unit FMs for divisions/non-divisional units. See this thread for my already posted material on the forgotten fact the Army decided APCs belonged to the Transportation Corps not the Infantry in this time period.
-5th MEB's table of organization for the projected Cuban invasion.
As for the USMC, while my work has focused mostly on USMCR units I do have a magazine from the Marine Corps University talking about the USMC's ready afloat forces in the Med through the 60s and 70s.
Short answer to that question is that there was a divisional tank battalion assigned permanently to each USMC division, each had a permanently assigned assigned heavy tank company with M103s. The Marines used them like big medium tanks, IIRC. The Force battalion was formed irregularly. It was a temporary formation to be employed with the FMF units afloat, which were ad-hoc units in this time period.
The Army, on the other hand, had separate doctrine for their (one) heavy tank battalion(s), to be used to assault formations or fight Soviet heavy tanks. One of the suppositions in my is a program to field convert M103A1s to the diesel M60 engines when available.
USMC also had Ontos (lightly armored, tracked fighting vehicles with six 106mm recoilless rifles strapped to the outside) equipped Anti-Tank battalions, one per-division.
For those with a British interest, there's the FV4202 and Centurion Action X concepts, revived when time ran out on what would have become the Chieftan.
While the British Army was unable to complete development to deploy their next generation “Main Battle Tank” because of wartime pressures, they were able to execute a substantial rebuilding program for their existing Centurions and new production of a much less audacious “new” tank.
The “Action X” was formally the Centurion Mk. 7/3, a designation that hid the radically redesigned turret applied to these hulls. Armed with the 105 mm L7 gun in a mantletless turret originally intended to be used for researching the new un-named main battle tank, it was instead rushed into production as an incremental improvement for existing stocks of Centurions to improve their lethality and survivability. While originally trialed with the old 20-pounder, production turrets carried the new 105mm gun.
In contrast, the FV4202, known as the “Cohort” or “Super Centurion” was a new design that drew from the older Centurion design, departing widely in an attempt to draw the lines for an improved tank to fight the IS-3. It was half a meter lower in height, with better sloping to its armor, and an even more modern version of the mantletless turret design.
Unfortunately, both of these designs inherited the problems of the older Centurions. They were two thinly armored to face most current Soviet armor, the suspension could be difficult to repair in the field, and even with improved sloping. However, its 105mm L7 gun was an excellent weapon for the time period and would give a good showing in the Twilight War.
There's also my crack at the BAOR's nuclear equipped artillery forces.
24th Missile Regiment, Royal Artillery: Barker Barracks, Paderborn
2 Heavy Battery (8” howitzer)
34 (Seringapatam) Heavy Battery (8” howitzer)
51 Missile Battery (Honest John)
76 Missile Battery (Honest John)
27th Guided Weapons (Corporal) Regiment, Royal Artillery: Napier Barracks, Dortmund
6 (Arcot) Battery
23 (Gibraltar) Battery
39th Missile Regiment, Royal Artillery: Dempsey Barracks, Sennelager
19 (Gibraltar) Missile Battery (Honest John)
36 Missile Battery (Honest John)
75 Heavy Battery (8” M115 howitzer)
169 Heavy Battery (8” M115 howitzer)
47th Guided Weapons (Corporal) Regiment, Royal Artillery: Napier Barracks, Dortmund
3 (Corunna) Battery
4 (Sphinx) Battery
50th Regiment, Royal Artillery: Northumberland Barracks, Menden
15 Missile Battery (Honest John)
21 (Gibraltar 1779-83) Missile Battery (Honest John)
33 Heavy Battery (8” howitzer)
78 Heavy Battery (8” howitzer)