Loaded tires, fronts and rears, are quite common as ballast on tractors.
Your tractor will uses a UTF/JD 303 equivalent oil. This is available nearly everywhere.. wally world.. TSC, and most of the 'big 3' tractor stores have thier brand.. NH m2c134d.. JD and case have hytran and hyguard.. etc...
That's for the tranny, diffy and hyds.. pow steering if you have it too.
Engine oil is a bit less specific.. but many like a 15w40 diesel spec'ed oil. Let your temperature of your environment help you decide onthe crank case oil viscosity.. etc.
Soundguy