I have run through a couple of different tire combos through the years with Moonshine. I'll do my best to remember the specs for each setup correctly.
CMCC 2008 - stock springs with long AALs at all 4 corners. Springs mostly flat. BFG 33x10.50 on stock 15" rims:
Right after doing the SOA with stock front springs (still long AAL) and ironman 2" lift springs in the rear with the overloads taken out. Tires are half wore out 36x13.50 Mickey Thompson Bajas. First pic is from a park in Kentucky, then from CMCC 2009. 15x10 wheels IIRC:
Moved to 35x12.50 MTRs on 15x8s IIRC with the same suspension (more settled now) in 2010, then to a new frame with the same setup in 2011. I broke a lot in 2010.
Moved to NC and kept the same setup for a while:
Put on some 37x13.50r15 pitbulls on 15x10 wheels, then changed out the body. By this point I'm running stock rear springs and wore out front OME springs to get her level.
Same springs, but now with 37x12.5r16.5 tires front and rear. Rear axle is a one ton at this point, but I've still got the stock toyota front axle, and the same tires front + rear:
Now I have stock rear springs in the rear and stock rear springs up front as well, so this suspension won't apply to many people. However, this is how a 37x12.5r16.5 looks with a J6x body (Loaded pic - gross weight ~10,000#):
Finally, for wheeling tires, I'm now using 39.5x15.5r16.5 Super Swamper TSLs on 10" wide rims:
So there's a pretty good selection of choices for you. Feel free to ask questions about any stage and I'll remember as best I can.