This. OP, I know you don't want to hear it but the 4L60 really is the way to go. Guys online fight doing the 4L60 all the time when in reality, it's far harder to keep the 700R4 and make the TV cable operate correctly (there's no truly good way to get it to work with a throttle body). You already have to buy a harness, so just get one that has the control capability for the 4L60 built in and you're good to go. Just make sure to grab the TCM out of the donor as well.
As for the torque converter, that depends on what you're doing to the motor. Keeping it bone stock? Keep the stock converter. Stock in an NBS truck (99-07) is something like 1400 stall speed (stall speed is where the truck actually begins to move once the revs come up). That with a 3.73 rear gear will cruise like a stock truck and still have a little pep when you step on it. If you're gonna slip a cam in it, then you need to match your converter to the cam choice.
Here's a good video of how a torque converter works:
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For example, when I first built my truck I grabbed an LH6 5.3 out of an '06 GMC Envoy Denali and slipped a BTR Stage 4 V2 truck cam in it for some chop and performance gains. I decided a Circle D 2800-3000 stall would be about right. I also wanted a little more oomph than my friends with 3.73s so I went 3.90 gears. That was a PERFECT combo. Put 27.5k miles on it before I swapped in a stick shift and never wanted for more or less gear or cam. It cruised at 2250 at 70mph and got 18-22mpg on the highway. The stall converter honestly could've been a touch looser, it would surge at stop lights if I didn't have my foot on the brake enough (with that particular cam, with a milder cam it would not have done that). In hindsight I would go with a 3400-3600 stall with that cam.