You should always try to get the smallest possible rim - to get more gum under the car! 17" is the smallest size, because of the break disks.
Please note too that the Landcruiser 200 are sold different around the world, which brings other Tyre Sizes with, who are possible without further modding:
US/Australia: euquiped with KDSS Suspension
Europe/South America: with AHC (active height control).
With the european AHC you can fit
LT285/75R17 what is 34". As you can see behind the link that I did query for lexus 570 Users - they all have AHC and was able to anser my question better

In the Picture you can see 33" on 17 Rims (285/70/r17).
Bigger is better is NOT true. The car is done for a given tyre size, the suspension, the gear-setup - tons of engineers did try to do the best setup for your car. The best compromiss between tarmac, gravel and offroad. If you want to stay with that, stay at the original 31" Size and enjoy.
To add bigger tyres means a completely different feeling: less power, less brakes, automatic transmission is working more and you odometer shows the wrong speed. Your spare tire dont fit below, you had to add a rear wheel carrier - and have to remove the wheel each time you want to open the rear door.
- You can work on the gear shift ratio
- You can adjust the speedometer
- You can add better brakes
But because bigger tyres lift you a bit, it will make the side tilt angle worse till you will topover. If you ever will be on the german highway with your car, your vmax will be limited through the lift who comes with bigger tyres. Most of us 33" or bigger tyre drivers would not be able to change a tyre and to lift the faulty tyre with rim up to the rearbar carrier without help.
It is possible to do bigger sizes like 33" or 34, with mods even 35" - but the car is then more for rock crawling than for cruising on roads. Your car is not same capable after start modding. It will need time, other mods and money, to get a part of the capability back. It may be better offroad, but not same capable on tarmac.
If you want to go the modding path - have fun! And keep the eyes on the terrain you plan to travel mostly!
If you ask for the best offroad tyre - we should look for the profile (AT / Mud Terrain) and the differences between the different brands... Even there. Doing a 1000 miles road trip with MT Tyres with 55 miles on the highway - hell it is pretty loud after some hours.
Surfy