It all depends...
You say no frame modifications, but then it sounds like you are going to have some that you are not planning on.
Power steering may, or may not, use the existing holes. Depends on what your get for power steering. That could be a frame modification.
You are asking about choices in axles and transfer case, sounds like drivetrain is not picked out yet, that could be more frame modification.
Paint and powdercoat are two different processes to apply two different coatings. Paint goes on as a liquid, cures as it dries. And there are all different kinds of paint. I don't mean colors, there are all different shades and colors as well. Some that should never be used on a vehicle (water colors, latex) and others that are good choices (Urethane and Enamel). Some are better for a final finish but would be a horrible chassis paint (lacquer). Or if you are trying to hide rust from the next owner, and you hope they don't know about it, shoot it with bed liner. So many different ways to go. And what are you trying to do? Win a custom car show where the frame is as clean as the perfect body? Or you just want something to cover the bare steel so it doesn't rust?
That was just paint. Powder coat goes on as a dry dust. Goes into an oven and is baked. Turns to liquid and the powder (powdered plastic) melts and flows out. Once cool it leaves a plastic shell over the steel. Nice, pretty durable, but still not perfect. Like paint, rust can creep in between. And you can't touch up powder coating. If chipped or gouged you are either getting it all stripped back to nothing and recoat from scratch, or you get a paint can and do a touch up.
As for best differentials, or so many good choices. How large is your budget? What are your plans for using it when done? How much power? How large of a tire? A Dana 30 might be a good choice for some, a Dana 44 is generally the go to choice, and the Dana 60 is the hard core option. Even then it also matters about getting the right one. Not any Dana 44 (for example) will work. Only one from from an early Bronco is a direct fit. Then there are the full width options.
And rear axle, countless flavors of the 9". From the mildest of the low GVW small bearing stock all the way to insane.
Transfer case. Again, what are your overall plans? Dana 20 that it came with is generally pretty good. Atlas has always been a go to choice for way better than stock. Most any modern chain drive transfer case (say 1980 and newer) is too wide to fit in the frame rails.
