I think it's important to at least own your email domain, so you can keep your address when changing hosts. Hosting myself is too much of a hassle, so I go with PurelyMail. It's wonderfully cheap and works great. Had no issues with delivery so far.
It's been a reliable (for the past 4 years I've used it) solution, with easy setup and laughably small cost. Currently it costs me about $0.3 per month to host personal mail for multiple domains (only one having some moderate activity in fairness).
All of these are mostly personal emails, I haven't tried to send large amount of emails to test their outgoing policies.