Assuming you have power disc brakes in the front with the 8 lug bolt pattern, a NP-435, with 3.73 or 4.10 gears, the largest I would run would be LT285/75r/16s . I ran this on a Dana 44 HD (4x4 van) and had no problems buried to the hubs in mud sometimes. Though I did not run a locker, if I ran a locker, I would keep it to the LT265/75r/16s. You might want to check out the treadwright retread tires in the mud D pattern with the kwedge rubber. It does pretty well on and off road.
As for the gearing, HP, and torque and viewing it for a mostly street vehicle, on my 390 4x4 F-100 (I think 4.10s) with the NP-435, the sweet spot for the tires was 31s when towing, especially starting on a steep incline towing a car trailer. The FE is an awesome engine, probably one of the best built by Ford is the FT, but, not a lot of HP or torque stock and when you start getting to 33s it takes it out out of it's sweet spot for power.
FWIW: Ford never offered the 390 in a 4x4, 360 was it, though that is not to say a 390 was not swapped in. Many just have an air cleaner that says 390 swapped in.
