A private and secure messenger is a messaging app that should not collect any information or message in any shape or form, and that must use a known form of encryption (like PGP for example). And it must be end-to-end encryption, or you can say bye to the app. Most people fall for the trick of "it's secure because the messages are encrypted", but before falling for that, take a look at what the encryption is. If it's some unknown thing and it's not e2e (end-to-end), don't trust it, if it's known and e2e, be less suspicious about it. But wait! Let's dig deeper and see what messaging apps we find, and see if they are good or not, shall we?
To start with, this one is a pure joke. It is owned by Facebook, one of the biggest privacy violators out there. It claims to be end-to-end though, but at the end of the day, it's them (WhatsApp) generating the keys, so it's not even real e2e. Also, WhatsApp got massively fucked because of updating their ToS. So really, avoid this app. It's clearly not worth your time.
Telegram is yet another messaging app claiming to be secure and private, however it literally asks for your phone number to sign up. It's like you stick a piece of paper on your head where you can read your address in big text. That's just so stupid, yet people are falling for it. But of course, that doesn't end there, as Telegram uses their own unknown encryption. There might be a few advantages there, but really, it's just as dumb as trying to make your own electronic circuit with just a piece of scissors : it will fail at some point or another. But anyways, as an old Telegram user, I can say it's your normal messaging app : chatting, friends, etc... Like really, nothing new from it. So stay away from it, because it's not worth your precious hours.
Signal is a messaging app that literally blew up not long ago, because it claims to be secure and private by design. However, it's actually... somewhat true. Signla has actually been independantly audited and that there's no backdoor at all. However, Signal still requires your phone number and is still centralized, and just because of that I cannot recommand it. Still, if you use Signal, you're not in big danger, or well at least for now.
To be continued.