As a rule, CAPTCHAs should be a last resort. They tend to be annoying, often aren't human-solvable, most of them are ineffective against bots, all of them are ineffective against cheap third-world labor (according to OWASP, the current sweatshop rate is $12 per 500 tests), and some implementations are technically illegal in some countries (see link number 1 from the MUST-READ list). If you must use a CAPTCHA, use reCAPTCHA, since it is OCR-hard by definition (since it uses already OCR-misclassified book scans).
It is possible to prevent browsers from storing/retrieving a password with the autocomplete tag for forms/input fields. However in the real world, your customers will have many accounts on different systems; it compromises their security if they use the same password for every site. Can you expect them to remember different passwords for every site? There are some good password managers out there, however there are also bad ones - which will become a target for attackers.
After sending the authentication tokens, the system needs a way to remember that you have been authenticated - this fact should only ever be stored serverside in the session data. A cookie can be used to reference the session data. Wherever possible, the cookie should have the secure and HTTP Only flags set when sent to the browser. The httponly flag provides some protection against the cookie being read by a XSS attack. The secure flag ensures that the cookie is only sent back via HTTPS, and therefore protects against network sniffing attacks. The value of the cookie should not be predictable. Where a cookie referencing a non-existent session is presented, its value should be replaced immediately to prevent session fixation.