In the 40+ years I have grown them...
I would normally prick them out and put into 3 inch pots, they would stay in them until it is time to live out in the greenhouse full time and then transplanted to 10litre pots (but depends on variety)
I use standard everyday compost, dont over water just damp. I feed mine once every 2 weeks with Maxicrop seaweed liquid feed(brown bottle)
I would normally use this through the growing season until fruit are appearing then I swap to plain old tommy feed.
Chillies are pretty tough plants and dont need masses of care or weird and wonderfull watering systems. I water every other day standard watering can.