Browser privacy when signing up: if I sign up for a service using a veee-peee-in, is there a best practice to make sure the site is not fingerprinting me by my browser, OS, resolution, etc?

I have recently become more worried about personal online security, like most in this subreddit I guess. I have just been using a private window on firefox or chrome, but I am sure there are better options. What can the websites see about me?

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