Key facts
If Brave feels like it's too close Google, Firefox is the way to go. It's built by Mozilla, a non-profit organization that has been around since 1998. It's built on their own engine called Gecko, which has zero Google code underneath. That independence matters more than most people realize when they're thinking about browser privacy.
Out of the box, Firefox is good but not great. It blocks some trackers by default, but you'll want to spend ten minutes in the settings to get the most out of it. Enhanced Tracking Protection to Strict, changing the search engine to DuckDuckGo, and installing uBlock Origin will give you a great setup to use Firefox.
Then there is Firefox's telemetry that is on by default, turn these off in the Privacy and Security section. Once you've done that it's one of the most private mainstream browsers available. However, if you would rather just download a browser and not worry about changing settings, there is Waterfox and LibreWolf. Both of these are built on Gecko, but have stronger out of the box privacy settings.
The extension ecosystem is the best in the business. Because Firefox has been around so long and has such a strong developer community, virtually every privacy extension worth using supports it. uBlock Origin in particular runs better on Firefox than any Chromium browser — that's not opinion, it's a documented technical difference that matters.
That being said, the trade-off is compatibility. A small number of websites are built specifically for Chrome and will behave slightly differently or break completely on Firefox. It's rare, but it does happen, and if you run into it you'll know. For most people and most websites it's not an issue.
Firefox also syncs across devices, has solid mobile apps on both iOS and Android. The Android version supports extensions, which no other major mobile browser does. That's a big differentiation if you care about blocking ads on your phone. The iOS version is a little more restricted, but that comes down to Apple forcing every browser to use it's WebKit engine.
The bottom line: if you want a browser with no ties to Google and full control over your privacy settings, Firefox is the one.
