I'd imagine so, but I don't really like peat moss. It's not a sustainable material, plus its a highly acidic and inhibits bacterial growth. I've never used perlite.
Pea gravel is different in different places. Take a handful of yours, wash it real good, then put it in a cup/bowl/whatever with some vinegar. If it bubbles, then it will cause you problems (it'll raise your pH levels). If it doesn't, then it should work fine for you. I read that peat moss will be a problem as it breaks down. I don't know about perlite, vaguely remember reading something that said it was ok, but I wouldn't trust that without other research.
Sorry, I'm not going to be much help to you. I'm just putting together my own first system now. Just wanted to share the knowledge I found while researching.
For the system I'm building, I am using a flood and drain method. It was the first method I learned about, so it seemed like the right way to go. :) Considering possibly adding on a floating raft system later on to grow more lettuce type stuff (chard, kale, spinach, etc). Way down the line, I thought I might try to find a way to integrate a wicking bed system into the AP system to grow potatoes and peanuts (and carrots, depending on how they grow in the f&d media bed).
Mine is outside, so I don't need a light and haven't researched that at all.