I think the answer partly depends on whether you care about the sub parts of of the ISBN-13, for example searching on books in a certain country or publisher. it also depends on whether you need to support ISBN-10 which allows for the character X as the check digit.
If you store as a string then I would suggest you remove any non-digits to formatting separate from validation.
There is a GTIN validation lib you might find useful too since an ISBN-13 is a subset of a GTIN.
