Firstly recognise that different countries have different needs, experience and therefore different solutions are acceptable. The continental only states - Benelux Germany Denmark are different from the US UK and France who have out of area commitments in spades and will require forces useable in Africa the Far East. Canada and the US are across the Atlantic, Italy behind the Alps.
So do the simple things first. Bomb shackles, refueling systems, the size of truck beds, containers and palletized systems. Recognize that folk will want to promote their own industry and their own industry will want to make a living. It really does not matter if different armies use Mercedes, DAF, Renault, Bedford or Fiat trucks as long as they can all fill up and accept the same size cargo or later on use different radar systems but they can plug into a common architecture and control system.
Without going too far off piste into what might have been.
.270 rifle ammo with a FAL probably EM-2 cos Rules, MAG and accept the French will be using their ammo until the late 50's or so and its the next gen rifle and GPMG that will be chambered in common. Pistols do not matter.
MBT is Centurion initially after that, Leo 1 and AMX are a dead end. Vickers 1 MBT is intended as a low cost Centurion, when you get to the Centurion replacement a JV between Vickers and KraussMaffei to replace the BRD M48s with earlier buy in from other European countries to get a Vickers/KM Leopard say Vickers turret KM hull which gives a good enough power weight ratio for the Germans and more armour, and the British accept a less heavily armoured vehicle but upgrade the turret to 120 rifled and after the Yom Kippur war that turret is the basis for one mated to the OTL Leo 2 hull and armament and armour upgraded to Valiant2 over time. The US will still give away M60's and M48s rather than pay shipping back to the US but there you go.
AT weapons CG, Milan, HOT. Swingfire, cover the period as OTL. If in doubt buy Swedish.
APC/light armour. There are two good families depending on where you stand. The British wheeled Saracen Saladin etc, and the AML series are different but fine early on, Later the VAB series or if you want tracks the FV101 series ( scorpion and derivatives).
IFV the VCI as a start point after which its likely to be common hull, turret to taste.
Naturally there would be local tailoring but having some component and sub assemblies in other European countries is less of an issue that across the Atlantic.
