I'd agree with the others here. A crate engine will be your best bet to swap in and go for it's sheer simplicity. Just be sure to look over your cooling system and flush your heater core, power steering pump and clean up the engine bay a bit before installing the crate engine. You can install the GM hot cam in the L31 350 SBC if you go that crate engine route, but you'll need the crane cams 747-16 valve spring retainers and keepers so that it will clear the vortec head valve guides. You can run that cam as it's a roller cam if your crate motor is a roller block but be sure to understand that if you run the stock MPFI injectors and black box PCM you WILL need a tune to get the truck to run well not to include a newer style Delphi MPFI upgrade. Black Bear performance can send you some materials to test drive your truck on so they can capture a data log on what the truck will need to get it running as good as possible. You then send them your black PCM, they upload the file and you're set for about $500 (prices may vary). If you choose to run a bigger cam in the end but not run a gm hot cam just be sure when you buy your crate engine that the crate engine will have heads that can run the size cam in lift that you're interested in and that you choose a cam that will match the blocks needs (hydraulic flat tappet or hydraulic roller cam). If you don't know what you're looking for will all the cam shaft and block lingo just call the manufacturer of the engine you're interested in and let them know what you drive, HP goals, the transmission you'll run, axel gear ratios, tire size and current engine (350 SBC L31). They can recommend a engine with that info and give you a price range on a direct swap or it's carbureted variant. I would expect to use up all of your $6k though with either endeavor.
I would also consider an LS swap over all other options as I've done a few in the GMT400 platforms and it's hand down my biggest bang for the buck and fuel mileage build for my customers. 350 HP with 24 MPG highway 16 city in a 96' C1500 on 22'' wheels. Truck is running these numbers with a rebuilt 03' LM7 5.3L, LS1 cam, 4l60e with a corvette servo shift kit and 3.73 gears. I know I'm on here always preaching the LS swap game but the aftermarket and big power lane is easy with the LS platform. Regardless, as many will say if you want to tow or keep torque numbers in the 1800-4500 rpm range, keep with the 350 SBC to get the truck the OOMF it needs to get moving quickly. Just my 2 cents on the conversation so far.