All of this information is based on the axle not being a tj Dana 44. If it’s off of a tj somehow all that’s needed is a new custom driveshaft everything else will directly bolt up. So limited slip will not cause any problems and you will not even notice it up front. Limited slip uses clutch packs to put pressure on the spinning side to help get the non spinning tire to spin. And it depends what Dana 44 you are using. jk44, 70s ford Dana 44… your options are endless. You are going to need a custom drive shaft and make sure they will fit your pinion yoke and the yoke coming off your transfer case. Next you will need to figure out your linkage. If you are not using a tj 44 then you will either need to do custom 3 link, get a truss that re uses the factory links then your control arms you have right now will work, or get a truss for a 3 link front and you will have to make your own linkage. Next you will need to figure out if you want coil springs or coilovers. If you go coil springs you will need to weld new coil buckets on to the axle. Then you will need to weld shock mounts onto the axle. If you want coilovers you will need to buy mounts and cut the frame then weld them in then weld mounts onto the axle. Next will be steering, you will need to make some sort of custom steering which is not to challenging Barnes sells everything you will need to do that. Just watch some videos on YouTube and you can figure it out.
Then finally for the re gear, if you are running bigger tires then factory you should re gear both axles, read up on what gearing to use for your tire size then regear both axles to that.
This is everything I can think off of the top of my head. It sounds like A LOT of work but if you can weld then it will be pretty straightforward. Best of luck