Instant Messenger

My recommendation: Signal

Download: Google Play Store | Apple Store | Desktop

Why should you use Signal?

Privacy of your data. Signal does not sell, rent or monetize your personal data or content in any way. Furthermore, it does not store any of your data, which is not necessarily needed for the messenger to work (or may be legally required of course). (source)
Default end-to-end encryption. Every message and every call transmitted via Signal is automatically encrypted and secure from being read or altered by a third party. (source)
Open Source. Everyone can audit and contribute to Signals code base, which guarantees that the company behind Signal can not lie about how secure their messenger is and how your personal data is being handled or maybe misused and mistreated
Founded by the non profit Signal Foundation. The company behind Signal does not see you as their product, they don't have to earn money with you and your data. The Signals Foundation aim is "to develop open source privacy technology that protects free expression and enables secure global communication" (source).

Why not WhatsApp?

WhatsApp is owned by Facebook. Do I have to say more? The Cambridge Analytica scandal alone should have been enough, to show that Facebook can not be trusted with any personal data.
Closed source. Only Facebook knows how WhatsApp works. However, they use the open source end-to-end encryption solution Signal provides and enable it by default, so the usage of WhatsApp is at least relatively secure. Just not private.

Why not Telegram?

No default end-to-end encryption. This is a no-go. Everyone could possibly be reading your messages.
No end-to-end encryption for group chats at all. What???? That's even worse.
Closed source. Yes, they provide a public API, but their server side code is completely closed.

Disclaimer: By trying to keep this page short and simple, I have simplified technical descriptions and/or made ~~very~~pretty generalized statements. Please keep this in mind.