So, if I publish a book series, should I choose ISSN over ISBN?

To clarify matters, a series of books is only eligible for an ISSN if it has no planned end to the publication schedule. Book series, like Harry Potter, Lord of the Rings, Chronicles of Narnia, are expected to end, hence not eligible for an ISSN, whereas institutional books like Encyclopedias, Concise Physics, Chicago Manual of Style, are continuously-improving series that do not have a planned end, and therefore is eligible for an ISSN.