I mentioned in my first comment that Chromium is the project, and Chrome is a specific (and official) build of Chromium. So you need to understand that Chromium is the codebase, and Chrome wraps up that code and distributes it (with minor changes) to the public.

Now you can still compile Chromium as-is at the trunk, without those small changes, but there's not an official binary as provided by Google for "pure Chromium". That needs to be compiled manually.

On Linux, you'd typically use your package manager to keep up to date with the latest builds of Chromium. If you're on Windows, again there's no official binaries but there are sites that auto-build the latest releases.

Nightly: https://download-chromium.appspot.com/

Stable: https://chromium.woolyss.com/

I'm guessing these do not include an auto-updater.

You should also understand that the difference between Chrome and Chromium is not just "tracking" (user metrics and crash reports). Chrome also includes content that could not legally be included in Chromium due to licensing, such as H.264 and AAC codec support. Those are pretty important to the web today.

I don't generally recommend running pure builds of Chromium except for developer use. You might consider an alternative like Ungoogled Chromium, though understand they focus more on privacy than security. You will lose features like auto-complete, browser sync, and Google's Safe Browsing service which warns of website malware. For this reason you'd actually be sacrificing security for privacy, which runs contrary to the goal you laid out above.

From all the information you've given, I do think a stable or beta branch of Chrome is your best option (though not Canary or dev branches, which are too recent).