These are best practices to remain anonymous while searching and browsing. You can check the anonymity of your browser by visiting https://coveryourtracks.eff.org.
Your internet service provider / cell provider knows what sites you went to, but (these days) not what you did there. If you use a VPN, they do not know what sites you went to. This includes public wifi.
Cell providers know approximately where you are, even if you turn off location services.
Websites know a whole lot and sometimes can pinpoint an individual even without knowing who that person is (fingerprinting, see coveryourtracks.eff.org)
Your computer has an identifier that goes with its network card, called a MAC address. Wifi hotspots will know this at least temporarily and possibly longer.
No: Chrome, Edge, Safari, Bing, Google search, gmail, outlook etc etc. All these companies will give all your info to the cops without them even asking.
Ideally log out of all those services on the device that you're searching with.
Whatever you use for the day to day, don't use that. Use some completely out of the box, uncustomized browser. Firefox or Brave are good enough.
In that browser, do not log into anything like your own email or Amazon or whatever. Keep it absolutely separate. You can reinstall or reset to defaults if you mess up
Firefox and Brave will clear cookies and history for you, but check that they actually did it. This is what "private browsing" or "incognito" type tabs do.
Is it the best search out there, probably not, but it's fine. Second best is to use Google or Bing with a VPN, from a browser that is not Chrome or Edge.
The Hegseth Principle: Signal is only as secure as the people using it.
The point of Signal is that the messages disappear, the app doesn't keep records, and the messages are encrypted. HOWEVER
If your phone is unlocked and Signal is unlocked, everything's right there in the open. It doesn't matter if it's encrypted on disk or in transit. That's how Signal works, at the end of the day human eyes have to read it.
VPN means all your internet activity goes through some other server, and that server sends it to you. Proton does not keep records of what it sent to where, and it is outside of the US so out of reach of US law enforcement. Nord is probably also ok.
That other server can be in one of a few countries (more if you pay for it). When searching it is sometimes important to remember where you look like you are.
The free version is fine but there are features that are worth paying money. VPNs are legal in the US, you can pay for it any old way.
Don't worry about this too much, but ideally be logged out of any other service, like things that might automatically check mail or notify you of stuff.
Why: because that other app will be keeping logs (records). If you have Facebook running and suddenly you look like you're in Sweden, Facebook will say oh hey this person was in Sweden for a hot minute and write that down. Later if law enforcement was looking at activity from Sweden, and also looking at you in particular, they could put this together. This has happened.
You can buy it and have it in your name. Just don't use it for any regular internet usage. This is just to make sure you don't have anything app on it that can identify you, nothing running in the background that you forgot about or accidentally logged into.
Bonus points though, buy used and pay cash. Then throw the damn thing out if you want to. You can get a laptop on fb marketplace for 50 bucks.
All data is connected, but you can make it harder for people to find and that might be enough. Why? Because investigations cost money.
REAL burner phones, like pay as you go, bought with cash, etc, are pretty hard to pull off. Cell towers always know where that phone is, so if you turn it on at your house or the same place as your regular phone, it's not anonymous anymore. There might also be a store picture of you buying it. Basically forget it.
It's really hard to be anonymous when paying for things, other than cash. Buying used or from a third party helps though.
Cell companies keep the actual text of text messages for much shorter than they keep the data about who texted who (metadata). How long varies by provider.
Computers have another identifier called a MAC address but this can be handled.
Phones are computers and have the same anonymity issues PLUS being on the cell network, but this can be handled
Public wifi is good, especially if you don't have to login (maybe at a library). In combination with other measures this can be ideal.
Good practice to encrypt your hard drive on computer. I don't know if you can on phones.