1) I would go with the 4.88's since they would give you just a little more torque to the ground over the 4.56's.
2) Not sure which brand is best (I did a full F/R axle swap to Dynatrac when I upgraded mine). I'm sure gear sets are just like everything else in that you get what you pay for.
3) The only thing I can think of on the carrier replacement is if you can't get the gear set you want for your axles. I believe your stock setup is Dana 30 front and Dana 35 rear. Some things to think about on this: Look at upgrading your axle shafts (going to deeper gears is going to put more stress on your axle shafts). Look into finding some Rubicon take off axles (you may find that the 4.10 gears will work for you and at the very least you may have more options for gear sets).
4) Since you already have the axles torn apart for a regear you may as well throw some lockers in, will save you the hassle and labor cost if you decide to do later. Even if you're not rock crawling lockers are a good idea. Unfortunately you won't know how good of an idea they are until you need them and don't have them. The main benefit of lockers is that they allow you the option to operate your Jeep with all four wheels actually providing traction.
5) As noted above, the axles shafts will take more abuse with deeper gears paired with larger tires. Another thing to look at is your drive shafts. Pretty much everything I have heard/read is that anything over 3.5" of lift requires drive shaft modification. Also, not sure if anything has been done about it, but the first few years of JK's has some problems with the front axle tubes and/or knuckle C's bending under the extra strain of larger tires. Most of this came in with 35" and larger tires, you are currently setting on 34" tires so you are right on the edge but this may not even be a problem if you are not wheeling hard.
I would go for a Rough Country stabilizer if for no other reason than to keep the suspension components common. Otherwise the stabilizer brand is wide open to opinion.
Here are some sites and information for you to play around with:
Gear ration calculator Gear Ratio Calculator
allows you to do a side by side comparison of two different setups.
Numbers for the above site:
Auto (5 speed, 2012-????) - W5A580
Gear ratios for the W5A580 (5 auto) are: (1) 3.59, (2) 2.19, (3) 1.41, (4) 1.00, (5) 0.83, and (R) 3.16.
Manual NSG370 (close ratio)
Gear ratios for the NSG370 (6 manual) are: (1) 4.46, (2) 2.61, (3) 1.72, (4) 1.25, (5) 1.00, (6) 0.84 and (R) 4.06.
Transfer case - X/Sport/Sahara: NV241, 2.72:1 low range or Rubicon: NVG241OR, 4:1 low range
This site just converts tire sizes DML Tire and Wheel Calculator