[LS short box]

I've done both gen3 and gen4 LS swaps. Really about the same amount of work. Gen3 engines are 14 years old best? If I was going gen3 I would buy a high mileage 6.0 for cheap and build it. Forged rods and pistons and cam. Add L92 or LS3 heads. Easy 450 rwhp.
If you decide on the gen3 the ecm will control the engine and trans. On a gen4 engine you need a ecm for the engine and the trans ecm. The gen3 dbw requires a controller while the gen4 requires just the correct gas pedal. On my gen4 swaps I deleted the VVT. The gen4 engines I've used didn't have DOD.
You can run FEAD from trucks and they are almost free. Change out the truck oil pan as needed for your swap.
All my LS swaps I purchased aftermarket harness's designed for my LS swap combo. Plan on buying some type of scanner in case of a check engine light.
Trans wise I've used only 4L60E or T56. The 4L60E's were rebuilt with "good" parts and had no failures even behind a 500 rwhp 427 cube gen3 LS.
Good luck with your swap.