Clip-in, or cleated pedals, where the shoe attaches to the pedal, improves pedalling efficiency dramatically, so is the preferred option for most riding styles, particularly if you’re doing longer distances.
Road pedals are a clip-in system that will only work with road shoes, which have a hard, flat sole. Very efficient for pedalling, very difficult for walking in, so go for this system if you’re riding on road only, and don’t need to walk around.
Mountain/hybrid clip-in pedals work with mountain/hybrid shoes, using a smaller cleat to allow a tread to the shoe’s sole. So these are the best option if you want to be clipped-in, and either go off-road, or have the option to walk around.
If you’re doing more technical, aggressive mountain biking a flat pedal, for easy escape is normally preferred. These are also a good option if you’re new to cycling and don’t want to be clipped-in, or don’t want to wear specialist cycling shoes.