You know, everything in a Jeep is a compromise and going big becomes expensive and is not necessarily better.
The only practical reason for 35" tyres is to increase axle clearances by 3". The required body lift should put the frame up about 6" - 9" and improve entry, departure and break over angles significantly. However it is not all good, as that requires a lot of money to get it right.
You need to fix the Jeep first, then tyres, wheels, flares, brake lines, brake upgrade if you want to stop, pitman arm, lift kits, steering change to power steering, steering upgrade to heavy duty, frame reinforcement around the steering box, maybe driveshaft changes, and maybe axle (one piece axle shafts in the AC20 would be a good idea with 35" tyres) and transmission upgrades (if you have an SR4 transmission it will not last), regear at both ends, and (if you want performance) even an engine upgrade.
At the end you will have a taller CJ with much better clearances off road but it will be slower and more noisy on highway. With those big mud terrains, it will take more than twice as far to stop in the rain so a good job that it travels slowly. Those darn compromises.
In fact you could put a lot more on there, just look at the builds on this Forum. Start making a list of what people have done and you will see that a top end 35" tyre and 4.5-6" lift is easily $5000 in parts plus labour without changing the engine. If you are not doing it yourself then $$$.
Plenty of shops will do it for you but hopefully you will fin out from this Forum what will work and what is a cheap arse build. You can do a cheap arse build of course but it could be horribly compromised.
For instance you will note that all in most of those pictures of CJs with big tyres they are sitting partly outside the body of the Jeep. The tyres should be sitting outside because of the turning radius of a CJ is determined by the front tyres. Those big tyres restrict the movement as they hit the leaf springs, so the stops need to be adjusted to keep them away which in turn restricts the turning circle. the wheels therefore need to move further out.
If you do not then go on a twisty trail and you will find it difficult in sharp turns. Solution for a good lift is either new wheels with greater offset or wheel spacers and wheelarch flares to cover them up. It is illegal in most places and inconsiderate to have tyres stick out from the bodywork so those wheelarch flares are not just for show.
These Jeeps were designed for 29" tyres. With stock suspension you can fit 31" tyres and your only cost is a set of tyres, the 8% change in gearing will not hit too bad on the highway and the turning circle will not be too bad, throw in some wheel spacers and flares and a narrowtrack CJ7 becomes a very wide track with tight turning circle which will get plenty of places.
See Puthijeep which sits on 31" tyres with wider offset wheels and narrow flares, turning circle is a PITA sometimes. Bagusjeep below, 31" tyres, wheelspacers, more offset on the wheels, large flares, can turn in a lot tighter than any rig with 35" tyres.
Cost of each upgrade was much less than $1000. I paid something like $3000 for each CJ and never felt the need to put in a lot more as they are very capable for what I use them for, which is poor condition highways, rough tracks, trails and beach visits. I need some clearance and 4x4 low range and a small amount of carrying ability for the surf board, beer etc. The other money I have put in was for fixing rust, long term maintenance, spares etc.
If you need all that clearance for your usage or just like the look, then start to plan for what you need and the $$$$ you need to spend. Doing something twice is just a waste of cash, for instance 33" tyres and then 35" tyres. For instance when I purchased my J20 it came with 35" tyres which were horrible and slow, it just runs better with 33" tyres.
