Ok... let's talk types of setups.

There are two basic methods for supporting the plant and providing space for the roots:

Media based systems - A media based system uses some sort of soilless mixture as a substitute for dirt in which the plant roots can grow and support the upper part of the plant.

There are any number of types of media one can use ranging from expanded clay pellets (marketed to the aquaponics market as "Hydroton") to pea gravel. The two things you have to concern yourself when setting up a media system are weight and PH neutrality. Hydroton is ideal in that it is relatively lightweight, reusable, and PH neutral. The down side is it costs an arm and a leg. Pea gravel works quite well, is cheap, and readily available. The down sides are weight (a cubic yard weighs more than a tone) and you have to be careful about content. All rocks are not created equal. Limestone, for example, will slowly break down and raise your PH so you will have to constantly monitor the water and compensate.

Raft systems - This is basically a sheet of foam insulation that will float on top of the water with holes in it. You place a small cup with spaces through which roots can grow in those holes with a small amount of some sort of media in the cup to support the plant stalk. The up side is it is cheap,  very easy, and lightweight. The down side is it is less flexible as you are limited in where you can plant to where you cut the holes. Also, since it has much less surface area that the water runs across it does not provide as much filtration nor as much area for the good bacteria to grow on.

Water flow

There are also two basic types of water flow

Constant flow - In a constant flow system the water runs in a continuous stream through your media or under your raft

Ebb and flow - In an ebb and flow system the water is allowed to fill up to a certain point then drain out in a cycle ideally lasting somewhere between 15 minutes and an hour. The plus side of the ebb and flow system is that with each ebb cycle you pull air down into your media which keeps the "bad" anaerobic bacteria at bay. The down side of the ebb and flow is that it adds a small amount of complexity to the plumbing.

Which is better? Ebb and flow vs constant flow... Media vs raft...? Well, this is the stuff of religious debates. I can only say give each a try and decide what is best for you.