If you want to stay anonymous, linux in general is the only viable choice. I donno about Ubuntu though, perhaps they send some data to canonical but it's probably anonymous at least (unless you have logged in to their services).

Also note that any website that uses fingerprinting can easily spot you across ips as well. There are browser plugins for that. But for the best privacy I would probably use a specific browser for my private browsing on some linux distro and of course not be logged in to anything while I am browsing the web anonymously.

Even better is to get a specific computer you only use for anonymous usage and also to connect to the Tor network after a VPN connection (that you paid with cash of course).

That way, it will be really hard for anyone to connect you to your real identity.

Mullvad is the only vpn provider that I trust because they actually let you be anonymous.