Shakespeare actually have lots of books that contains lots of poems. Romeo and Juliet would be a good way to start as a beginner poem reader because it is actually a easy play/book. The prologues and the meeting of Romeo and Juliet is actually a form of poem call sonnets.
You can find the pdf here: (I don't really know any available books with poems in them)
https://kenstonlocal.org/fodor/wp-content/uploads/2014/08/Romeo-Juliet-Script-.pdf
