It really depends the reasons for your interest. If your intent is simply to gain an acquaintance with some well-known stories, then any generic textbook on myth will do: your choice should be determined by what's cheaply available. This would be the one circumstance in which I'd recommend Powell's Greek Mythology (don't bother getting the most up-to-date edition: it's one of those textbooks that gets re-edited constantly to prevent students from buying second-hand copies; more recent editions are not superior to older ones in any way), a book which for any other purpose I regard as despicable.

For reference purposes almost any encyclopaedia of myth would do, but I particularly recommend Jenny March's Dictionary of Classical Mythology published by Cassell.

Now, if you have some more specific purpose in mind, whatever that purpose may be, the recommendations will change. If it's to improve your understanding of mythological references in modern-era literature and art, then the book you want is Geoff Miles' Classical Mythology in English Literature: A Critical Anthology, or perhaps Karl Kilinski's Greek Myth and Western Art.

If your interest is in the theory of myth then, to be responsible about it, you need to engage not just with the myths but with the contexts in which they appear. For that purpose a general textbook like Powell's one will be worse than useless. You'll need to familiarise yourself with the types of sources that transmit the myths to us, the purposes for which the myths were used, and the ways they developed and changed over time. As a n aid you'll need an encyclopaedia of myths that consistently includes detailed references to primary sources. In English, a good recent one is Jenny March's one (see above); a more exhaustive one is William Smith's 3-volume Dictionary of Greek and Roman Biography and Mythology, published in the mid-19th century; still more exhaustive is Roscher's German-language Ausführliches Lexikon der griechischen und römischen Mythologie (1884-1937), also available online. Here's an older post where I give links for online copies of Smith and Roscher.