...since I personally have never gotten a vehicle (new or used) with anything but street tires (including all terrains) on it, I have always had to apply adequate rubber before hitting the tails (my trail preference is moderate to difficult).
My personal preference is for smaller vehicles the following may not apply to monster trucks.
A first concern is gear ratio, because it has a great affect on drivability; many vehicles are geared excessively high from the manufacturer. I actually got a Jeep once with 2.72 OEM gears and another with 3.08s; for gearing in this range sticking to the OEM tire size is normally best as oversized tires (i.e. 33s or larger on a smaller SUV with stock gearing) will almost always result in poor all around performance.
IMO, a FUN to drive vehicle is very desirable; you should be grinning when you get in and out of it.
Accordingly I have gotten a bit of experience changing gear ratios and setting up differentials... (It can be quite spendy to pay someone to do this).
Note; drivability is highly subjective but here are my preferences; manual OD tranny; 33inch tires 4.27 gears, 35 inch tires 4.56 gears... automatic trannies can get away with a slightly higher axle gearing due to transmission slippage when starting from a stop; 33s are considered livable by some with 4.11 gears and 35s are ok with gearing in the 4.56 range (note 4.27 gears are often quite hard to find, especially for newer axles). Note; extremely under powered (<200 HP) low torque (<200 lb-ft.) vehicles/engines may feel better with lower axle gearing. Setting the vehicle up to cruise on the highway near the peak torque RPM seems to work pretty well. Excessively large gears (i.e. 4.56 with 33 inch tires) will result in excessive/not optimal highway rpm, and running excessively large tires with too small gears will result in having to shift out of over drive for small hills or not being able to use it at all. It should be noted that very high torque high horsepower engines can work acceptably with more of a mismatch than smaller engines, in my experience.
The next concern is axle strength it is possible to overwhelm axles with larger high traction tires; make certain (do research) that the axles are more than strong enough to take abuse off road with larger tires.
Adequacy of brakes; larger, heavier, tires and rims will increase the load on the brakes and stopping distance; its simple physics (for tires larger than 33 inches on a small SUV; 4 wheel disk brakes of adequate capacity should be considered, IMO; note this is highly vehicle dependent as some vehicles have much less adequate brakes than others).
Finally comes fitment;
For some vehicles a small (~2") lift might work for medium sized tires. I personally abhor large lifts (>4-5") because they can make the vehicle unstable (even dangerous) to drive; if a lift greater than 4" is thought to be necessary body modification should be considered, IMO.
Based on some poor experience, in my youth, with wheel spacer/adapters; I cannot recommend them. If the wheel off set needs changing for clearance or to keep the tires from rubbing in a turn; possibly rims with the proper offset can often be found. Note; offsetting any tire rim combination from OEM specs will affect the axle bearing loading, again do your research.
Enjoy!