I have used hover.com, originally netidentity, since the 90's for my personal email. That gives me a user within a domain, not a whole domain, but has been trouble free. It originally had a web site bundled with it but that part got spun off to a separate company, which can be confusing come billing time.
Since then I have also used krystal.co.uk for a family domain, as many email users as I like, web site, all sorts of software options configurable via a web based control panel.
It is certainly a good idea to have addresses independent of your connectivity provider, I wouldn't have been able to keep the same address for 20+ years otherwise and it reduces the effort involved in switching providers.
