I've got a 360 with a mild cam, T150 3 speed and I run a D44 rear and D30 front with 3.73s. Both axles are 100% stock (from a '73 CJ6). When I first swapped the motor (before the rebuild and cam) I had the original D30 front and AMC 20 rear with Moser shafts and 3.54s. The 20 only lasted 2 weeks. Grenaded the spider gears doing a burnout with 33s. I drive the D44 the same way and have had no problems.
The stock axles will get you around if you're easy on the gas and don't go over 33s. If you upgrade I would look into a D44 front (wagoneer, scout, or narrowed Chevy) and for the rear either a D44 (wagoneer, scout) or Ford 9". D60s are strong, but unless you run big tires, you're going to lose a lot of ground clearance.
77 CJ-7- AMC 360, Edelbrock cam, MC2100, Fenderwells, CJ T18/D20, Chevy D44/EB 9" rear, Trutrac f/r, 4.11, SOA, 1.25 lift shackles, 35x12.50 BFG KM2s, Shackle Reversal