Anyone Tried Library Books on E-readers?

I am debating on whether to get a Kindle Fire or some brand of tablet. I like the idea of a larger screen but it would not be as portable. From what I understand, the Fire will download from a local library but I don't know about any tablets. I certainly do not want to have to buy ebooks. They are more expensive than a paperback. Has anyone had any experience with these electronics?? I need some advice, please.