Email client alternative to Gmail with app, webmail & IMAP?

Hello everyone,

I currently use Gmail as my email client and receive emails via POP3 from:

• GMX
• Web.de
• All-inclusive
• Domain Factory

Now I want to leave Gmail behind because:

• It's annoying that Gmail only checks via Pop3 once per hour
• I have to integrate another mail provider that only supports IMAP (and Gmail only supports Pop3)

What alternative could you recommend to me?

My requirements would be:

• There's a webmail client (I'm just not a fan of installed software)
• There's an app for Android
• You can store various IMAP accounts

Optionally, I'd also be willing to set up a home server for this – but then I'd have the same requirements 🙂

Thank you in advance for your answer!

David