Looking for a storybook from my childhood - early 50's printing? Collection of stories?

My mother had a book from her childhood from which she used to read to my brothers and I...I remember some of the stories: The Gingerbread Man, the Chinaberry Tree (in which a girl climbs a tree and teases pers-by, gets stuck and has to wait for someone to get her down...I think her name was Lula?). There were also several poems, including Twinkle Twinkle Little star and Rock-A-Bye Baby. All were heavily illustrated. This book was about 3/4 to an inch thick and had a yellow cover. Ours was unfortunately destroyed by a roof leak - by the time we discovered the leak, the section of books was too moldy to save. Does anyone remember reading this type of book? It was originally bought for my aunt, who was born in 1955, so I'd say it's copyright date would be mid to late 50's? Thanks so much!!