Was Shakespeare an actor or a playwright?

Both, actually, but a playwright for a living.  He played a few roles for his theatre group, Lord Chamberlain’s Men, including (possibly) the ghost in Hamlet.  But his canon of plays, especially as documented in the 1616 Folio and its opening endorsements by other theater figures in the Elizabethan and Jacobean periods, makes it abundantly clear that Shakespeare spent his entire professional life as a working playwright, well known and universally respected for his products for the stage.  In addition to his theatre work, he also wrote poems, mostly but not completely sonnets.  He has adumbrated dozens of his contemporaries, such as Christopher Marlowe, Ben Jonson, and Thomas Middleton, all very competent playwrights but virtually forgotten outside academia.