The difference basically comes down to how you feed your plants, organic nutrients or chemical. You could start out with a peat based mix like Pro Mix that is mainly sphagnum peat moss and perlite, then add organic amendments like worm castings, composted manure, etc. Or you could take that same Pro Mix, not amend it with anything and use liquid organic nutrients and it would still be considered an organic grow. But the same Pro Mix with chemical nutes wouldn't be.
Three gallon pots are a good size for autos. If memory serves me, you were planning using on a 2' square tent. You could probably fit 3 in there. If you went to smaller pots, say 2 gallon, you could probably fit 4 but your plants would be smaller, so would yield less. Some people like to start their plants in the final pots to avoid transplanting. I prefer to start in a smaller pot, then transplant after they sex. That's partly because I grow a lot of regular seeds, so I'm not committing 3 gallons of soil to a plant that could be a male. I also prefer the smaller pots to start since they will dry out quicker, allowing me to water/feed at more regular intervals.
One technique you might want to consider is called The Tiered Method. Take some large party cuts, preferably 32 oz. or bigger and cut the bottom out of one. Take a second one and poke a few drainage holes in the bottom. Place the one without the bottom inside the one with the drainage holes. Fill it with soil and start your seeds in them. When they are big enough to go into the final pots, simply remove the outer cup and "plant" the one without the bottom about half way deep into your final pot. The roots will grow out the bottom of the cup and fill the pot. Using this method there is little chance of damaging the plants during transplant.