Depends if you are interested in scholarly approach or general approach.
In those books, I range those who are both fun and informative, while not being horrible 600+ pages books without illustration in 10 size fonts.
The everything classical mythology, affordable and fun to read; Offers a cover of the Greeks myth from the Gigantomachy up to Troy.
The complete idiot's guide to mythology. Another fairly simple and fun book to read. it's an Idiot's guide so don't expect too much, but nice.
Classical mythology & more. Another good and easy entry level book. This one, contrary to the first two, actually cites a lot of sources, and the juicy passages. this is overall a damn fairly good and solid book while of easy access. Note also it is designed with teaching in mind so in a way fairly great for a learner (there is little exercises at the end of each chapter).
D'Aulaire's Greek myth Fairly classical, not especially my recommendation.
Graphic Universe, if you love the way the D'Aulaire's are working you can check this wonderful graphic novels series, as for example Odysseus. As the series in its whole is covering a lot of myths you can gain a high knowledge of Greek myths.I am not the biggest fan of comics (eon of) and just read Odysseus which is "accurate". I would favor those over D'Aulaire.
Those books are if you are interested. Lots of texts, few images, this is the fairly serious matter.
Early Greek myth, Timothy Gantz, you have everything there, sources, literacy; this is the defacto starting book. There are 2 volumes, and definitely NOT a beginner's guide. If you want a gentle introduction, refer to my general section.
Greek religion by Walter Burkert. Just note the author is German, and I pointed you to a translation. Burkert IS a must read, providing the subject interest you. Another extremely good one to read is Structure and history in Greek mythology.
Art and myth in ancient Greece T.H Carpenter, which offers a beautiful reading of myths and arts, here and there you see me using arts or hieroglyphs to explain this or that. While not a compendium, that is a fairly useful tool for you. Even Gantz or Burkert are not especially art oriented.
Greek mythology, an introduction by Fritz Graf, another German guy (learning German when you love myth is FAR from a bad idea, fact is learning English, German and French is pretty smart). This is less aggressive than Grantz (only 300 pages) but still should be read.
The Metamorphoses by Ovid, if you are looking for THE reference, you have it. Not only it is filled up to the root with mythologies BUT, cherry on the cake, it is one of the best poets on Earth who wrote it... you find there lots of alternate versions (read the myth of Romulus and Remus to see Ovid's giving you his opinion with subtlety)
The Penguin's dictionary it's some Penguin's material, solid, well written a good source and reference.
You can add DukeZhou's Hamilton && Oxford book.
The Greek myth by Bob Graves. Lack of seriousness for the myth part and for the poetic aspect I would pick Ovid anytime. Quite cited here and there (especially here). If you have time, only (I just gave you 4000 pages. Not to mention the Greek/Roman authors. Come to me after Homer, Hesiod, Herodotus, Thucydides, Plato and Plutarch... Roughly 10k pages before Graves).
Rick Riordan. We saw Rick Riordan cited here and there here. While not a pejorative comment (at all), Riordan is a novelist writing and assuming writing novels. He cannot be considered a Greek source, either than "In Rick Riordan universe... blablabla" (I consider an answer beginning by that totally acceptable). I know Riordan published a compendium on Norse mythology, I have not checked it at all.