You can use the rear end, but you ought to get rid of the spool. Look at Quicks performance for a clutch style posi and new axles to fit the posi spline. That would be cheaper and easier than getting another complete assembly.
Regarding the transmission. A TH400 will work just fine perhaps, repeat perhaps. It depends on how it's built. You should know if it's harsh shifting from driving it. You mentioned a PT converter. I assume you meant a PTC. If it is a PTC, then that's a quality unit that could be re-stalled for a more street friendly amount of slip, or it might work just fine on the street already - again, it depends on how it was built. But re-stalling is pretty inexpensive. An OD, like a 4L80, would be great, but not cheap between the transmission and the controller to run it.
Regarding the carb and MSD box (yikes - I've never understood doing this to an LS, but that's me). It would be a super easy conversion to a Holley Terminator TB or Sniper TB setup, but another $1000-1500 of money. Putting a multiport on it can be more expensive if you want an aesthetically pleasing intake.
And I can't disagree with
ck80, selling the entire driveline to someone 'in the know' of what it is might offset the expense of swapping . Or just swapping the trans and rear.
Personally, with being cheap the main target (because I am), I'd 'run what ya brung' and put a Holley on it with a Terminator Stealth TB with the MSD, different differential, gears and axles. That should be in the $2500ish range. We are all very good and spending your money haha. Do you have a budget for this project?