Hi Jeff,
25pdrs were the standard Field Artillery piece of the British Army. There's no real way to avoid them, though in the very early part of the war there were still some 18pdrs knocking around.
Mountain Artillery Regiments were equipped with 3.7-inch Mountain Howitzers, though these served mainly in the Far East and Italy (and were almost all Indian).
Light Artillery Regiments were again equipped with 3.7-inch Mountain Howitzers, though were motorised and had guns with pneumatic tyres instead of mules and wooden wheels. These were mainly in the Far East and Italy, though one such regiment served in NW Europe.
Jungle Artillery Regiments served exclusively in Burma and were a mixture of 3.7-inch Mountain Howitzers or 25pdrs and 3-inch Mortars.
Airlanding Light Artillery Regiments used 75mm Pack Howitzers.
Although not officially artillery, being part of the divisional MG Battalions, 4.2-inch Mortars were found in all divisions in Italy and NW Europe.
M3 75mm GMCs were used by some Armoured Car Regiments in NW Europe, as well as almost all Armoured Car & Recce Regiments in Italy as the regiment's own 'pocket artillery'.
No, the Commonwealth didn't use halftrack-mounted mortars, though some units in Italy and Burma employed Indian-Pattern Wheeled Carriers as SP mortars and the Australians produced SP mortars based on the Universal Carrier. I've also seen some photos of locally-modified Universal Mortar Carriers in Burma.