Firefox is a good platform for privacy-conscious browsing, but it's not geared for privacy out of the box.
The "do not track" setting is a farce, you're probably better off not setting it.
Without going into the details of each extension, I use NoScript, Cookie Monster, Request Policy, uBlock Origin, HTTPS Everywhere and Random Agent Spoofer to reel in the browser's behaviour. By using the former three in a whitelist configuration, you can explicitly manage permission to execute scripts, store cookies and send HTTP requests, much in the same way you explicitly give permission to contact a server when typing a URL into the address bar.
Encryption serves to guarantee that nobody but the intended recipient can decode your traffic, but HTTPS Everywhere is not really an encryption tool as it does not guarantee encryption. Also, Firefox uses your system's DNS settings so your DNS has to be secured separately. Therefore, beware what, and to whom, you send.
It shouldn't have to be said, but none of this protects you from explicitly sending personal information to parties wishing to exploit it. For example, it doesn't prevent you from explicitly supplying Google with your life story through their search engine.
If you want anonymity, it must also be provided separately. Servers you contact know your IP address, which can be used to either build a profile on you (marketers like Google do this) or uncover your identity through legal action. If this is an issue for you, a VPN or Tor can be used to provide anonymity if used carefully.
The FOSS nature of Firefox and its active ecosystem probably makes it the best choice for private browsing, but the same could be possible for other browsers. Just make sure to use a FOSS browser as your base platform.