Well first things first. your link is not pointing to an NFT system. Its either deep water culture, aeroponics, or a hybrid. I don't know which. I didn't read the instructable. I just looked at the first picture.
Having said that, I believe you should stick with the system shown on the instructables site. it is more suited to what you want to achieve.
as far as advice for that system on instructables, I will say;
make sure you have a drain valve in and an opening at the top of the reservoir. lifting the lids on larger plants can be a bit tedious.
make sure you used a reservoir basin that is either light tight or paint/cover it with something that is. this will help tremendously with algae growth.

Looking at it, I thought it was an NFT system of sorts because nutrients are pumped from the bottom to the top container and out of a spray bar and then drain back to the bottom container.
Would pretty much any growing medium work for this?

Don't get hung up on the terminology as everyone has different names for the systems.

I stay away from organic media as it will rot eventually. Cocoa coir is organic.

the only thing that system will use media for is to hold up the plants while they're getting established. peppers are generally smallish plants, so a large enough pot should hold them up through the life cycle (maybe a 3" pot) I have traditionally used river gravel as my medium. this year I've used lava rock (bought at lowes then crushed to size with a hammer) and marbles. Looking at how things are going, I'll probably stick with marbles in the future. they're a lot easier to disinfect and recycle since they're smooth on the outside.

I'm familiar with the design you linked, it's technically an aeroponics system, but as willard said the terminology isn't really important. It's a good functioning design.

I'm a big fan of Advanced Nutrients stuff, and for peppers make sure you don't go too high on nitrogen or all you'll grow is a big, green bush with lots of leaves.

Here is a link that might be useful: AN products