On all my desktops and laptops, I use Firefox ESR with the arkenfox user.js to shut off what annoying parts of the browser’s functionality I can. I also use ublock origin, umatrix, clearurls, and decentraleyes to break most websites by some amount. When I can’t figure out how to unbreak them, I switch to a less hardened profile that just has ublock origin. This works for a single user who won’t get scared and frustrated when something goes wrong, but not for a multi-user system wherein any user can be on any computer. I still need to get some idea about how I can get that to work.
Other browsers I’d consider:
Pale Moon
Great in theory, I have no idea how often websites don’t work on it. Allows Xul extensions to work.
Waterfox and Waterfox Classic
Forks of firefox owned by an ad company, sold off without telling anyone. Practically, not worse than Firefox if they follow development of Firefox close enough, but who even knows. Classic also allows Xul extensions to work.
GNU Icecat
It wants to be the best at privacy, security and freedom. It doesn’t have enough developers to keep up.
Librewolf
Forked from more recent versions of firefox. who is behind it? No idea! Has more attention that Icecat.
Ungoogled-Chromium
Works as advertised, but hyped as THE only morally conscionable option by people who, I can only imagine, want anything not based on Blink wiped from the face of the earth. You’ll need to compile it to be sure you’re getting what the code says you’re getting.
Tor
A specific tool for accessing sites in a certain way, or reaching .onion sites. Many sites will reject you for using tor, be it system-wide or just through this browser.
For AOSP ROMs (do not use base android or an iphone if at all you can help it):
Fennec
Works kinda okay on newer hardware. Unusable on older phones. It’s not as good as it used to be.
GNU Icecat
Works better than Firefox or Fennec as far as stability goes. If you run into a website that doesn’t work, you’re probably using your phone too much.
Android System Webview browsers
They’ll perform better than either of these, but you’ll need a system wide ad blocker to disable a significant amount of the tracking the web otherwise does.
For Linux phones:
Firefox
Some UI elements are kind of a mess right now on my pinephone, but you can bring in your desktop profile folder and it’ll work.
everything else:
Basically okay but you can’t disable unwanted web functionality very easily.
Browsers I won’t consider but aren’t really out to get you:
Falkon, GNOME Web, and Konqueror
These just don’t, as far as I know, have the ability to block out as much of what I want to block from the web as I want.
Brave
I mainly don’t like it because it’s blink based and due to that whole crypto thing they’ve got going on (that’s optional) and some users of other websites I know of have been spamming it ad nauseum. A lot of people seem to think its basically fine once you change a few default settings.
Dissenter
A tool for leaving comments all over the place that few will see. It’s not safe to tell people you use it. You don’t need the browser because the browser extension still works. It’s just hard to find packaged for installation. But you can install it directly through the update URL obtained from the extension’s manifest.json here or here. I wish someone would fork it so it could work on fediverse sites that didn’t disable the activitypub API (unless I’ve completely misunderstood how it works).
If I didn’t mention it, I either don’t know about it or it’s best avoided.