The 1500 w/ 5.7 - check your door sticker because you are pushing the max capacity with it.
Capacity changes with transmission and even gear ratio and depending what you have you might max it there
If you are going to tow that much just a couple times a year and not through mountains on the hiway, you can get away with it. If you are towing that often, you bought the wrong rig. To do it safely and not have everything break down all the time you may be pouring thousands of dollars into it.
4L80e transmission in it? What gear ratio?
Leaf springs & shocks (no struts on these) are only a part of it. Brakes are my biggest concern.
Wilwood makes a brake kit that is $1,500 for front axle, and a rear disk conversion that is $1,500 for the rear axle. So there is $3,000 to get you better -not ideal stopping.
You swap to different spring kit for the rear that are heavier duty but they raise ride height. Better is begin with new stock springs because the 30 year old ones are simply tired by now and won’t perform as they should. Then get a helper spring or imo the better move is the Firestone air bag towing kit. This way you aren’t changing the handling when not towing and when you do, just air up and it will take the weight without ruining ride. Those are $500 if you do it without an on board compressor. Adding the on board compressor tacks on $$ and just depends how much you choose to spend for it.
A set of new Bilstein shocks all the way around.
The transmission- you need to tell us what you have first. But realistically, most people run what they have until is starts slipping then rebuild. Most likely the 4l60e. You can search the online builders like B&M or TCI with a triple disk converter. If you have the 4l80e (unlikely) then it’s ok as is but when rebuilding is needed there is a few upgrades to do including the converter.
Adding a secondary transmission cooler is always a good idea to extend life, get a descent one not a cheap one. Also look into a manual override switch to force the lock up of the converter for when you are on the hiway only. Until you have a lock up converter and the switch on the 4l60e- anything other than flat ground you will manually downshift to drive. This isn’t a maybe type suggestion this is how to not call a tow truck.
For adding more power to the 5.7 there is a ton of options for that. A set of descent headers with an H or X pipe then duals out the back with high flowing mufflers.
Cold air intake.
The fuel cannon is a known hiccup issue- and replacing it with the first two items of letting it breathe properly is a standard action. There are tons of options, a hint is all the mid to low range cost one suck & will be replaced in 40,000 miles or less. Buy once cry once here.
There is a ton more possible with the engine but those basics will help it a lot, and depending how tired your engine is now- you can easily be running HALF of your torque/hp rating. And those all being external means they can be reused when it’s time to do the inside of the engine. Anymore it’s almost always better to order a long block from one of the major builders than redo your original.
What my best suggestion is to you - move up to a 200-2004 2500hd suburban with the 6.0 in it. It’s a world of difference.
I regret selling my 69 Camaro, and next in line is selling my 2001 K2500hd suburban. Zero modifications were needed to tow the weight you are taking about all day long. If mountain towing only additional is the transmission cooler.