Alternate Ship
If you're interested in using an alternate ship from the one you'd otherwise automatically start out with, try the following. At the title menu, hold the A and B buttons and press start with the buttons held. This will give you a newer, fancier looking ship to use.
Wormhole to next level
Do you see those metal mask structures that create plasma spheres that destroy all enemies when you touch them? There are 2 kinds. The ones that look like machines and the ones that have smiling faces. Shoot the ones that have faces to create a Plasma Sphere. Don't touch it until the white part of the sphere vanishes. Now touch it. You'll be instantly warped to the next level. Most levels have at least one. However, they're commonly placed in high speed areas or behind the mask ones.