[LS short box]

My .02 on LS swaps no matter what they go in.
I buy the aftermarket LS harness and computer from one supplier so if there is an issue I have one company to talk to. I've used Speartech and Howell with good success.
A 24 tooth reluctor LS engines needs one ecm to run the engine and auto trans. 58 tooth engines need two ecm's, one for the engine and one for the auto trans.
I would do a 5.3 and run a small cam. New push rods and springs.
Not many low mileage 2003 5.3's around. If you buy a higher mileage 5.3 I would do a new oil pump, timing chain and new rear main seal. Make sure you compression test it before buying and pull a valve cover to see if it's clean or full of burnt oil. On my C10 swap I used a fbody oil pan so it didn't hang below the frame cross member.
I used a Ididit column and it worked well.
I used a Painless chassis harness. Worked well. I hate 50 plus year old wiring. LS swaps like and need nice 12 volt signals to work well. Also don't skimp on good grounds.
I like to run the biggest radiator I can fit. I used a Afco LS swap radiator and Spal 16" fan.
If you are running a stock 5.3 I would do a mail order tune. If the 5.3 has some mods I have it tuned on a chassis dyno.
Again just my .02. Good luck with your swap.