Front is probably a Dana 25 or 27, rear is a 44, I believe with two piece 10 spline axles, not sure how strong the rear 44 is, but it's not the strongest. The front is weak from what I know, a Dana 30 from a later jeep is a decent upgrade for a relatively low powered jeep. If the front axle is stock, I'd be careful with tires as large as 35". I forget what the weak point is, might be the knuckles? But from what I've heard, they're not strong at all.
For the motor and trans, a Buick V6, and a 4 speed (granny first gear) is a pretty popular combo. Lots of info here on various transmissions, and they sell high quality adapters too.
Novak Conversions Home
If you want a diesel, I believe there's a few VW TDI swaps out there. I've also seen a few older Benz diesels swapped in too, but those might be a little too long for an old flat fender. Kubota turbo diesels have been done as well, but I don't think it'd be powerful enough for highway usage. Might be worth checking out the Willys section of Pirate4x4 for ideas.
Jeep - Willys - Pirate4x4.Com : 4x4 and Off-Road Forum
A modern 5 speed would be nice, but the thing is that the wheel base is so short, that you really need to think about how long your trans/transfercase package is going to be, or your driveshafts could end up being too short.
Regarding seats, since it was mentioned, the stock seats SUCK. Suspension seats of some kind would be a good idea. Or quite honestly, anything but the original seats. Speaking of, I don't know how tall you are, but older CJs are pretty limited on leg room. A lot of people cut a notch out of the rear wheel tubs to get the seats mounted a little farther back.