Deep water culture DWC. This type system is one pot with no reservoir. This is a nice place to start. I tell you what. If you don't like this style this next one probably isn't for you.
RDWC starts for Recirculating DWC. This style usually has more than one grow pot and usually has a reservoir. I think you could get by without it, but it's so damn handy I highly recommend one.
This is mine. The res. is out of frame, but there are my pots and lights.
Deep water culture is an acquired taste. Other than fogponics its probably the most demanding and it is SO easy to lose time, and possibly plants. Nutrients need to be taken seriously. The elements go straight to the plants. Unlike soil there is no buffering. It can also be crazy rewarding. Fast vegetation, a perfect root condition, killer buds.