Have you checked out the wiki? This page on progression looks helpful without being terribly spoilery if you don’t read too far ahead, and you can search the wiki for specific topics that you need more info on.
For getting around quickly, people usually build a skybridge (this can be a simple platform above ground that goes all the way across) to go horizontally, and a hellevator (shaft that goes straight down) for going down. Later you can setup a pylon teleport system to instantly travel around the world.
