One go-to app for folks who want encrypted messages is Signal. It’s available on iPhone and Android and is really easy to use. First you download the app then register your phone number. On Android, you can even set it to be the default messaging app (though again, you’ll want to make sure you’re sending messages to someone who’s also using Signal to ensure encryption.) When you send a message to someone without Signal, it will ask you to invite that person to use the app. Do this and your messages will be encrypted.
Signal also has additional security features including options to block others from taking screenshots, disabling keyboards that learn from what you type, and the option to set a password to open the app. There’s an option to make messages disappear after 5 seconds, which is convenient if you’re worried about someone going through your phone.
Finally, Signal shows you the “safety” number that you can compare with the person you’re chatting to to make sure that the conversation is secure.