While waves which travel within the depths of the ocean are longitudinal waves, the waves which travel along the surface of the oceans are referred to as surface waves. A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. In a surface wave, it is only the particles at the surface of the medium which undergo the circular motion. The motion of particles tend to decrease as one proceeds further from the surface.
Any wave moving through a medium has a source.
Somewhere along the medium, there was an initial displacement of one of the particles. For a slinky wave, it is usually the first coil which becomes displaced by the hand of a person. For a sound wave, it is usually the vibration of the vocal chords or a guitar string which sets the first particle of air in vibrational motion. At the location where the wave is introduced into the medium, the particles which are displaced from their equilibrium position always moves in the same direction as the source of the vibration. So if you wish to create a transverse wave in a slinky, then the first coil of the slinky must be displaced in a direction perpendicular to the entire slinky.