This is the one I personally owned as a child. As the very first, it is chock-full of the standard issue, top-20 pop charts tales -- among others. Heavily from Norwegian, French, and German sources.
Though even with the popular ones, he may include things you don't know. He follows Perrault in Sleeping Beauty in the Woods, and so the story does not end when she wakes up. Beauty and the Beast has significant dreams for Beauty.
And some ones not too familar. Why the Sea Is Salt. Snow White and Rose-Red, which has no connection at all to Snow White and the Seven Dwarfs. The Story of Prince Ahmed and the Fairy Paribanou. And more.
I really can not recommend the French ones here because they are all precieuse, and very literary. (Unless, of course, you want to see what the precieuses did with fairy tales.) Or A Voyage to Lilliput, on which Tolkien is right, it's not a fairy tale. But it has some interesting works.