I can recommend Fastmail. No affiliation, just a happy customer. I've used Gmail for several years previously and thought I'd miss it when switching. I didn't.
I also use Fastmail. No affiliations, just a content customer.
I pay for a mobile telephone service, but email is more important to me so my convictions necessitate a paid email service from a dedicated provider with a real support team.
I also own my own domain, primarily because now my email address is short and unambiguous to say over the phone.
Late reply, but I would recommend Posteo [1] because it's flexible and very cheap if you need multiple accounts. I switched to it a year ago to move out of Gmail and other "free" services.
Fastmail is, for my needs of a few mailboxes (each with its own credentials), very expensive - running into few hundred dollars a year!
Another similar and cheap alternative is Mailbox, which allows custom domains to be used.
Both the services allow IMAP, which was very important for me to have local copies of emails if I ever decide to migrate out.
Someone hijacked an older google account of mine, the phone number used had since run out and been sold to another user.
Google asked me to either have access to the phone number, and the old password, or to know the security question, have access to the backup email, and know the exact day the account was created on.
Google was not willing to provide any help, not even via the Nexus phone support, and even after a friend who worked at Google submitted an internal recovery form.
After I contacted the new owner of the phone number, and coordinated with him a way for me to authorize via SMS, backup email, old password, security question, and account creation date at the same time, I got back into the account.
In the account I found an email from Google's account recovery support thanking me for contacting them, apparently they had contacted the hijacker after I asked for help, not me.
After changing all data, I went through the login history.
The account was set to German, always used from Germany. Someone tried logging in via several different VPNs, and was blocked a few times, but allowed the last time from Russia.
I had learnt the account was compromised originally because Google sent me an email that an attacker from Russia had logged into the account and changed the password.
So, to recap:
Google realizes that an attacker connects and hijacks an account, emails me, but doesn't prevent it.
Google allows that person to change the password, and tells me that an attacker changed the password, but provides no way to restore it, and doesn't block it.
You can't restore with backup email, security question and old password.
Once Google's internal account recovery team was contacted, they talked with the attacker, not with me, despite being explicitly told I had no control over the account.
A random person was more helpful with restoring the account than Google itself.
Do NOT ever rely on Google, and write down your accountcreation date right now (on desktop, in gmail, settings, pop3 and imap, "pop3 active since" tells you the account creation date)
Asking for a phone number as a verification method is particularly toxic for users such as myself who do a lot of international travel and essentially just use phones for data plans.
Due to a close call with one of my own accounts, I absolutely refuse to link a phone number to any online account, for fear of it being required months later when I'm in another country. I still nearly gotten bitten by this problem when Google wanted to use my old android phone itself as a secondary identification method. AFICT, the only safe solution is to also avoid using Android phones (or have no Google accounts you'd care about losing).
Oh, the backup email worked. But to restore it's not enough. You need either
a) old password, SMS
b) security question, email , date of account creation.
And I didn't update the phone number because I had stopped using the account, and had forgotten about it (but I also obviously didn't want anyone to spam in my name, or extract my data).
Many stories have been posted here over the years of people whose Google accounts got disabled for some unknown reason, with no way of contacting someone at Google to get the issue resolved. A quick web search turned up this example:
Please please please stop using Gmail for important communication and account recovery (banking, mission critical services you maintain, etc etc).
Use a paid service from a reputable company who does that one thing only and does it well.
Too many Gmail horror stories.