Step 1: find a local friend to work with you.
Seriously, there is nothing more valuable than someone with a different perspective and some basic skills.
I would also strongly recommend going to an LS swap forum and reading about the ins and outs of that swap. You will need to either build or buy a standalone harness for that engine and get a tune to remove the VATS.
As far as your axle question, the 4x4 S10 axle will fit. Some had LSD, some don't. When you are at the junkyard, check the RPO codes and if it has a G80 then it is the limited slip.
As light as the truck is, a used 5.3L will easily spin the tires even with an LSD unless you put pretty wide meats on the back.
As a note of encoragement, I did my first LS swap with just the internet for help. It took me about a year and I spent about $2000 on it. That car is still on the road with that engine 15 years later.
Good luck!
