Please keep in mind that while schooling is mandatory only as far as OWLs, Wizarding law says you are underage wizards, as far as we know, until you reach the age of 17. That means if you do magic outside of Hogwarts before then, you are subject to punishment, up to and including the snapping of your wand. Dropping out of Hogwarts does not circumvent this, nor does choosing a career that heavily involves potions (which is a form of 'casting magic') or runic magic. Fred and George, for example, didn't drop out until after they were 17 and could apparate. For more information on underage characters outside of Hogwarts, read 'news school summer.'