Where do p and S waves travel? (Like through the earth, on its surface, etc)

The letters "p" and "s" stand for primary and secondary, but they can also be thought of in terms of how they move, p is for "pressure", and s for "shearing", the term "shearing" is a term that means the side-to-side motion of those waves. These waves are "surface waves", waves that travel on the surface of the Earth instead of through it.