Medium is what the plants roots will be growing in.

Coco coir is a good option to start with. It can be purchased in compressed blocks that need water or loose and ready to use. Mixed with perlite to improve drainage and aeration in a fabric pot works well with a saucer underneath. It is used in a drain to waste systems. Nutrients can be mixed and poured into the coco coir perlite mix with a watering can. Or a reservoir can be set up with a pump to drip over medium. Cannot be used in a recirculating system.

Coco Coir with Perlite

Clay pebbles are used in hydroponic systems with water. There are many different types of set ups and they require transfer or air pump or a combo of the both to drip nutrient solution onto the clay pebbles.