As
@Enot1964 mentioned, anonymity is relative – especially if your threat model includes an opponent that has the means to overcome the obstacles you put in the way.
OS:
I use a Linux distribution myself but if you really are paranoid about security, you could use an OS like Qubes OS, but that in turn will also require a somewhat decent computer to run the virtual machines inside of it. I have not tried Qubes OS myself so far but I guess that one would probably run into few issues when one wants to play regular (Windows) games with it due to virtualization.
Browser:
The Tor browser would probably the best choice but has the drawback that it might be slow, sites might straight up block you, or you will waste time of your life solving CAPTCHA.
Search engine:
Personally, I also use DuckDuckGo as a search engine most of the time.
Keep in mind that even when you use all the tools available to you, one can still run a profile on how you act (i. e. time of day being active) or write for instance.