IMO, codesertrat hit it nearly right on the head with 31 inch tires.
...some points... Tires are rarely the size specified on the sidewall (usually they are undersize diameter wise).
The rear wheel openings of my CJs and YJs, over the years, would not take a 33inch(size on side wall) diameter tire at full stuff without rubbing/damaging the tires and/or the sheet metal.
The largest tire that I have been able to use in a stock sprung CJ was an undersized 32 x 11.50 ... it would rub occasionally on the street but not enough to damage the tires or sheet metal (your results may be different).
IMO, the shock absorber mounting points of CJs need to be moved to enable the use of longer shocks (if difficult off roading is planned).
I have been universally dissatisfied with the ride given by "Heavy duty" or "off road" shock absorbers, for the stock springs and shock mounts I found that brand name regular duty replacement shocks (from autozone or other store) give the best ride, good life and reasonable cost.... find a store with a friendly parts guy/girl that will go through the boxes to find the right length if the springs have been replace with lifted springs or if they have sagged.
I like the ride that soft springs give.
If planning a spring lift try to get low spring rate springs and avoid stiff "lumber wagon" extreme arch lift springs.
For my '81 CJ-5 and my current CJ-7, I used stock YJ hard top 6 cyl. springs (lift kit take outs) in the rear I believe they have 5 leaves, avoid the YJ 4 leaf soft top springs they seem to bend pretty easily. Initially install the stock shackles then if necessary, make shackles to adjust the ride height give or take an inch or so from stock (adding 1 inch of shackle length will give roughly one-half inch of additional height. but do not use the shackles to try to get more than an inch of lift.
NOTE; if you wheel it hard YJ springs will eventually assume a W shape and sag but it normally take several years.
For those that want to use 33 inch to 35 inch tires with a compliant suspension I would suggest investigating cutting the rear wheel openings and adding TJ rear flairs (35s will necessitate slotting and bending the metal lip at the front of the wheel well and probably bump stop modification and lift springs).
To avoid loosing too much performance, I do not recommend significantly increasing the tires size more than 1 or 2 sizes over stock without re-gearing the axles to compensate.
Airing down is the cheapest, easiest way to get traction, but the tires should be aired up to highway pressure before getting back on the road (most carry a compressor for this). airing down a 16.5 inch tire wheel combination will probably result in the tires becoming unseated but no other size that I am aware of is as problematic; though tires at low pressure can become unseated in any size... just know and be prepared to reseat tires on rims (15 psi will normally retain the tires on the rims but only gives a marginal traction improvement)
Enjoy!