You might want to look at Fastmail.com, a paid e-mail service with actual customer support. They provide a web-based interface, mobile apps and also IMAP access, and you can use your own domain with it if you like. (I've been happily using it for a few years now, and first heard about it here on HN.)
ln addition to everything mentioned by others I also love Fastmail app both iOS and Android.. It's around 1MB in size on iOS compared to over 100MB for Outlook or Google Inbox.