Check your wheel ratings. Method makes a nice wheel called the NV305HD that has a 4500lb capacity per wheel, if your current ones aren't sufficient. A lot of aftermarket wheels have poor capacities. Also check your tire capacity - though most 35" tires should be higher in capacity than the factory tires, I've seen quite a few American Standard sizes where that isn't the case. Most metric sizes have higher load indexes. YMMV.
Be aware of your rear axle capacity, and confirm where you are loaded with the trailer, at the scales.
I wouldn't bother upgrading brakes on the truck. Upgrading the trailer to EoH disc, on the other hand, is one of the best safety investments you'll ever make.
I had the ProPride 3P many years ago, and it worked as advertised. Worth the money in my opinion. The biggest con is the somewhat reduced ground clearance because they hang low. There is also a slight learning curve to hooking up, but it's mostly mitigated with a backup camera.
I would not use air bags. They have a cult following on here, but are not all they're cracked up to be. A proper spring pack is the real answer, or helper springs like SuperSprings. I'm pretty sure the air bags they sell for the GM 3500s are all inboard of the frame, which will exacerbate sway, regardless of marketing or claims otherwise.
Your stock receiver should be fine, but double check the ratings. I think on my Chevrolet 2500 the stock receiver was rated for something like 14 or 15K.