FWIW, I think you can just get a Google Voice or other short-term burner number to sign up for Signal, and then never worry about it again. Signal's an order of magnitude more trustworthy than the other messaging players and have built out a good base of features at this point. (telegram specifically is a joke... proprietary closed-source encryption is a recipe for disaster.)
I would strongly advise against picking a tiny new-comer without some serious research beforehand... They're not battle-hardened, so will typically be less reliable than any of the existing larger players.
I don't think never worry about it again is quit correct
What if someone registers with my old number?
If someone were to register with your old number on a new phone, then they will have an empty message history. Your contacts will also be made aware of a safety number change if they start messaging with the old number.
I had no luck getting people to use signal. Family thinks that I'm a freak because I try to make them understand that in socialist Denmark your communication is not secure from the government.
The app is easy to use, but people are not using it. They use sms and FB etc. to message friends.
I would strongly advise against picking a tiny new-comer without some serious research beforehand... They're not battle-hardened, so will typically be less reliable than any of the existing larger players.