Movement of water at the surface gets you more oxygen than bubble surface area does. (So both the movement of surface water by exiting filter water and the movement by the bubbles churning the surface can achieve added oxygenation.)
Movement by your filter may be enough in the long run, but you may want an air pump and airstone for various temporary uses. I have extra airstones running in my empty tank trying to maximize oxygenation during fishless cycling as this helps with bacterial growth. I'll take it out probably, after I've finished preparing the biofilter and get fish. I think with various fish illnesses an extra airstone can help too.
Sorry that answer doesn't sound so simple! Have you been reading the fishless cycling article?
~~waterdrop~~