Well I was thinking around 30 to 40 inch and mainly mud and nearly vertical dirt road in the mountains
That's one heck of a range!
The list of things you would have to do to your TJ to fit and operate 40" tires is very long and extremely expensive. If my memory serves me correctly, I think the largest tire size you can go to on a TJ without a lift is 31". With a 3" - 4" lift, I think you can go to 33" or 35"... I have no first hand experience with this. I am just going off of what I think I remember my dad telling me when he was upgrading his TJ.
I can offer no help with the tires, I have only run BFG Mud Terrains and ProComp Xtreme Mud Terrains... both of which I am very happy with.