If you have an authenticator, you MUST enable the option to prompt you for the authenticator code at every log in. If you have this disable, it will only prompt you once a week which pretty much renders the product useless!
Additionally, the Battle net SMS Alerts are an extra nice feature with added security as well.
I personally recommend using both of them enabled.
Finally, I suggest turning off Real ID so folks won't see your real name and such.