A good book or source for climate science and meteorology basics?
Cambridge University Earth Sciences Department's reading list particularly suggests:


Pierrehumbert, R.T. (2012), Principles of Planetary Climate. Cambridge University Press, Cambridge UK, ISBN:9780521865562.
IPPC assessment reports
Cronin, T.M., 2010. Paleoclimates: Understanding Climate Change Past and Present. Columbia University Press, ISBN 978-0-231-14494-0


... plus many others, with a range of focuses, all of which are made explicit.

Other books include:


Physics of the Climate System, Peixoto and Oort
An introduction to dynamic meteorology, James Holton