Chrome definitely has the right answers in terms of privacy. It’s not perfect – nothing is – but it’ll do more to secure your browsing with the right add-ons than most others. The key thing is to use Adblock, Privacy Badger, and Disconnect – they add a lot to your experience.
In terms of passwords, a good password manager is LastPass. At $24/year, it’s not particularly cheap, but it’s pretty reasonable. The key thing is to have the password for your LastPass inscribed onto the inside of your eyelids – when you lose that, your only real recourse is to destroy the account and start over, and yes, that has happened to me. OTOH, that’s part of why it’s relatively safe.