Store is as a cookie. Localstorage and sessionstorage should be used for things like caching files etc. I.e. anything that's large. Where as cookies are used to store "small" sets of info, such as access/session tokens.
REST is more how you communicate between the client and the server. Localstorage, session storage and cookies are all just methods of storing data. Just be sure you parse your data correctly and you'll be fine :)