Tor Browser is believed to be the safest browser.
But Tor is not anonymous on its own.
People often confuse security, privacy and anonymity. Those are different principles, and each is important if you are under some kind of threat.
For best protection, it is recommended to use your own proxy server with Tor, preferably with a dynamic IP address, as the last hop. It mitigates the risk of interception by compromised Tor exit nodes, it bypasses bans and restrictions placed by many sysadmins on traffic that is coming from Tor, and it is even more technically anonymous than Tor itself. You should also learn how to configure Tor and Tor Browser according to your circumstances, as their default configurations are not completely foolproof. The anonymity will depend how on what setup you are using while accessing the TOR network. The TOR setup may, or may not, be completely anonymous, depending on a bunch of factors, some extremely subtle.
Tor is a good example of the deep web, but it’s not for newbies.
That’s why I’d recommend you to use MarketerBrowser instead which allows you to bind IP and fingerprint to each browser you create.