The roots grow where they grow. The still grow down and out but they are kept inside the tray once they out grow the net pot they started in. That is why you cover the tray to keep the light out of the root. (light will kill roots)

For your first attempt in hydro you would be best to try DWC. It's easy to make and maintain.

You do need to equipment for hydroponics that you did not need for dirt farming. So get ready to spend some money on a few things like Ph/TDS pen. Ph up and Ph down, and depending on the water you use some calmag plus, B1 and some other minerals that the plant finds in soil but not in hydroponics so we add them out self when we grow.

Gool luck