you want to start with a nutrient that is either balanced, like 10-10-10 or 20-20-20 or, barring that, something with a good nitrogen content, like 15-10-10. Later you'll want to switch to something with more phosphates.

don't start using nutes until the plants have at least got some side branching going, and even then only at 1/8 strength at most. You're going to gradually build them up.

I did the same style growbox, and my final pot size is 3.5gallons. I think it'll be sufficient. you really want something anywhere from 3 to 5 gallons, although a 5 gallon pot wouldn't have fit easily in my setup.

hope that helps, and good luck with your grow!