How to save my Apple ID password?

I have a new Mac Air - my third one.

When I sign into iTunes or the App Store, the system doesn't remember my password. I have to go look it up, then copy and paste it in.

My browsers offer to remember passwords. iTunes, the App Store, and iCloud don't.

How can I get them to fill in automatically? My computer is protected with a login password; Firefox won't fill in passwords unless I put in a master password at least once a day. So I'm not overly concerned about someone getting into my Apple account via my laptop.