I think you do it either way, but it depends on the medium. I dont think you could let an absorbant medium (e.g. Coco coir) just sit in the water.
I just keep the water level under the pots, allowing the roots to hang down into the water. I try to keep it very close in the seedling stage, but after the roots grow down to the water it doesnt matter as much.
Always run the pump 24/7. In water, the roots need to be provided with oxygen, which they usually get in soil all the time. You'll need an air pump, tubing, and an air stone. The more air to a container, the better growth rate/yield. My best plants get a shitton of oxygen.
You can easily make one. I've made alot of them
Just take a rubbermaid container, and cut holes out of the top for your net pots, which can be found online cheap. I have been using 6 inch net pots, but i think thats overkill, I want to switch to 4 inch for max efficiency.