40s will break many things on this Jeep. The steering system cannot handle 40s, and the brakes cannot stop 40s adequately. The frame can't handle the stresses that would be induced by 40s. The axles can't handle 40s. The engine...
This vehicle was designed for about a 50 mph maximum speed when it was new and all systems were stock/in good repair.
Best fuel economy? 28 or 29" tires. Clearly this size tire tends to limit the obstacles that the vehicle can traverse.
31s will be OK, but not optimum. You will get some rubbing offroad, and on-road hills will slow you down alot.
You'll need a lift if you plan to offroad with 33" tires, which are pretty much the max for the stock axles without frequent, expensive breakage. 33s are pretty heavy, and may cause some issues with the knuckles; consider going to knuckle studs in the D27.
This vehicle has 9" drum brakes. Marginal at best, terrible if offroading in wet conditions. Consider upgrading to front discs, 11" drums, drilled drums, D30 front axle swap, etc.
The factory steering in the '62 is a Ross box and bellcrank set up. This has many wear points, and unless recently rebuilt, is probably dangerous. Consider rebuilding the stock set up, or swap to a Saginaw system.
I suggest you spend many hours reading the information and posts at EarlyCJ5.com, a family-oriented site dedicated to CJ5s from 1955 through 1975. You'll find lots of great info there, but no support for putting 40s on this rig.
If you really want to run 40s, sell this rig and buy a platform that has a better chance from the start.