For ground forces, Standardize on 7.62x54R, 12.7x99mm and .45ACP. Standard rifle will be the SVT-40, SMG will be the M1A1, LMG shall be the Madsen gun, and the standard Squad MG shall be the Browning M2.
As for Artillery and Anti-tank gear, standard sizes will be as follows: Howitzers:105mm American and 155mm and Mortars: 81mm. Anti-aircraft weapons will be the Oerlikon, Bofors 40mm L/60 and the 90mm Gun M2.
As for the actual weapons, the 155mm Gun M1E1 and M12 GMC shall be the standard 155mm pieces, and the M4A3(105), M7 and M2A1 will suffice for 105mm. Anti-tank weaponry will be the QF-17pdr and Raketenpanzerbüchse 54.
Armor will be limited to the M4A3 family (some to be fitted with 17pdr ASAP, or given up-armored M10 Turrets,) M10 (to be upgraded to 17pdr SP Achilles ASAP) and Crusader, with the Crusader being limited to SPAA roles, alongside the M16 MGMC. the M8 Greyhound, M20 Scout Car, and T17E1 Staghound shall be in use as Scouting vehicles.
Logistics/Prime Movers:
M3 Half Track family, LVT-4, M4 High-Speed Tractor, Dodge WC series 1/2 and 3/4tons, and GMC CCKW.
Aviation Assets:
Tempest, Corsair, A-26 Invader, Vickers Wellington, and for Logistics the C-75, C-47 and C-54.
Seacraft: Provided by someone else most likely. Probably Flower or Castle-class Corvettes, Gleaves, Fletcher, or Allen M. Sumner class Destroyers, and River class frigates, along with some minesweepers. Maybe a Gato or Balao class if we get lucky. But LST 2 and 3s as troop transports, various MARCOM ships for everything, and a Vulcan-class and a Pair of Dixie-class for patching things up. An Escort Carrier or CVL would be nice, and a Cruiser like a New Orleans, or Brooklyn class would be useful for shore bombardment.