I've read this question: Chrome Extensions & Javasctipy Database but I want an answer with more details and more clear.
How can I store some of my extension settings?
Is there any good tutorial on it?
I don't want to use Local Storage, because I do not want the behavior of SESSIONS
You could use
chrome.storage.local (docs). Both are local storage (not session storage);
sync has the additional advantage that it syncs to the user's Google account if they've connected Chrome to it.