I ran the OME 2.5 + budget (pucks & shackles) = 3.5-4" lift with 31" tires for years.
I was able to run on about any trail. The only reason I would not go is that I wanted to keep my sheet metal straight. So I did not follow the buggies.
At this point I wanted to keep the rig look as much like stock as possible. So I had the stock bumpers and no trimming. I did have some armour. I wanted a capable rig both on and off the road but did not want to spend the money to work out the issues with large lifts and tires.
In the 3-4" lift range you are at the top end of what I would call the less expensive lifts. If you are lucky you can run at that height with none or a limited number of other suspension mods. You know... SYE, new track bar setup, control are relocation...
I was lucky and was able to run for a time mostly stock. Had a TJ slip yoke (slightly longer) and new LCAs.
Now on the the 31" tires. That was as large as I would go with the current gearing. They would tuck up in the fenders nicely. This allowed for plenty of up travel. I could limit that to where I wanted with bump stops. Adjustments on the shock mounts allowed good droop.
This size of tire was not a problem for the stock axles if you are not mud bog racing. Lighter tires meant good gas mileage and road manors. I was still commuting with it at that time.
I wanted to keep as much stock look as possible. For One I like the look of cherokees and Two cops do not bother you. With the setup most people though I had maybe 2" of lift. It was a well balance setup that hid the potential very well. No hate here. I just like the look on the faces of the people in 6"+ rigs when I would follow them over an obstacle.
The only thing I would have done different at that point would be to regear and run 32s. They would still be able to tuck in nicely. I personally think that 4" of lift with 32s is one of the best all around setups.
That being said I wanted large tires. I was looking at 33". So I had to regear. I went up another inch so I could fit true 33" (285/75-16) tires and still have some stock look. But you cannot hide that much lift with 33" tires. The stock flares are still on and mostly mounted in the same location. I had to trim 2" from each end of the front, 1.5" on each end on the back wheel wells and pick the correct backspacing to allow the tires to stuff nicely.
The large tires and lift force the addition of other goodies: CA drop brackets, SYE, Track bar, new rear axle...
Figure out what you want to do with the rig. If you care about how it looks figure that in too. Learn from others experiences...ask questions, read, talk and look at rigs. Plan and build. Have fun and drive.