anonymous browsers

hello, use to browse in anonymity tor browser or other browsers (whitch i don't know but imagine there are other in addition to tor for those who want only anonymity and who don't want to reach deepweb sites) to browse as a normal browser whitout special precautions, such as entering in sites whit credentials, both sites like forum or a bit more serious like **** to see the statements or use google as a search engine, enter the email and so on. if I do the things I listed above on a browser that guarantees anonymity, is it likely to lose such anonymity? if yes, how should I use that browser and which search engine should I use?

You can use Tor Browser is very anonymous and is very quickly