It very much depends what provoked your interest, how long your attention span is, just generally what kind of thing you're after. The AskHistorians book list on ancient-mediaeval Greek history is this way. Paul Cartledge's Ancient Greece: A History in Eleven Cities (2009) might well be my first choice, though it depends on taste.

(Edit. Just promise me you'll avoid anything written by Robin Lane Fox!)

For mythology, I'd recommend one of the following, depending on your preferences:

• On the development of myths and the roles they played in ancient Greek religion and society: Ken Dowden's The Uses of Greek Mythology (1992). Accurate, finely judged, gives due attention to historical context, but enormously interesting and (I think) perfectly accessible. (Also freely available on the Internet Archive, for some reason. Don't look a gift horse in the molars!)

• Collection of more in-depth/academic studies: the Blackwell Companion to Greek Mythology edited by Ken Dowden and Niall Livingstone (2011).

• An accessible, well-illustrated reference book/encyclopaedia: Jenny March's Dictionary of Classical Mythology (1998). Much better than any other English-language encyclopaedia of the last century.

• An anthology of mythical narratives, with little or no attention to historical, regional, or religious context: almost any old compilation will do, like Kevin Osborn's Complete Idiot's Guide to Classical Mythology, Joe Lee's Greek Mythology for Beginners, or even (*twitch*) Barry Powell's Classical Mythology. I find it difficult to mention any of those without physically shuddering, as they're so ahistorical and pay so little attention to where the myths actually come from, but for someone who's interested in the stories, not the history, they may be exactly what you're looking for. (Robert Graves' The Greek Myths is the worst of a bad bunch: that one is probably worth avoiding no matter where you're coming from.)