There are plenty of wonderful texts about the work of J.R.R. Tolkien which could be of value to any Ranger. And while you don't have to have read them all, there are a few that are more-or-less essential. Links will direct you to an amazon.com page where you may purchase the book, if you'd like, or to the URL in the case of online resources.
The Lord of the Rings, obviously, is the most important book any Ranger needs in order to roleplay effectively. Not only the main narrative, but the Appendicies (at the back of The Return of the King for three-volume editions) contain a wealth of knowledge that no Arnorian ought to be without. The more popular (and shorter!) The Hobbit contains nothing about Rangers or Arnor or Dúnedain in general, but is still a good read.
An Arnorian would be well-advised to pick up a copy of Unfinished Tales as well, which has the only real tale of Númenor within its pages, as well as background information that an Arnorian player could find very useful. Despite the name, much of it reads more like a collection of short stories than of disparate fragments, and it is easy for the casual reader to get into. The Silmarillion contains the best background on the ancestors to the modern Dúnedain and the First Age legends you will hear about regularly in Imladris, but on your first read be sure not to become bogged down in the parts before the main Quenta Silmarillion: the cosmology can be rather tedious and bears no resemblance to the main narrative.
Finally, the dedicated fan, or the one who wants to win every argument, will require the twelve-volume History of Middle-earth series, available in too many volumes and packages to ever link here, and The Letters of J.R.R. Tolkien. The former is a collection of rough drafts, concepts, early sketches, and the like, and the latter is a collection of letters. If you'd just like a quick reference to thumb through for various issues, Robert Foster's The Complete Guide to Middle-earth is the canonical choice, but it is far from perfect.