I use Proton Mail. I recommend that whatever service you decide on, get your own domain name so you can keep your email address if you move to a different provider.
Not OP, but I used Namecheap. Porkbun is also recommended I think. Setting it up is not dead-brain simple, but Proton does a very good job on explaining it step by step I believe.
IIRC Cloudflare is the only registrar that doesn't mark up from wholesale prices, or something like that. Basically makes them cheaper than most other registrars. I think the point is that they can then sell you their other (related) services more easily — the services that actually make them money.
By having a common email address that you give out to each service you sign up on you make it easier for them to aggregate the data and build a more detailed profile on you, in order to avoid it you would use email aliases (dummy address that serve the purpose of only forwarding emails they receive from and to one of your real address). If you use a custom domain name you can potentially create an infinite amount of them, but you expose yourself to being tracked anyway because they would all have the domain name in common e.g. [email protected], [email protected], etc. and they would notice that it all comes from one user for service, so it's easy to guess it is actually just one real person.
To avoid that happening, you would have to use a public aliasing service so you can blend in with the other users
Any decent email hosting service should allow you some form of aliasing (whether it's plus addressing or actual aliases). Ideally there should be no "default" address associated @your.domain, it should be all aliases. Preferably with wildcards so you can make them up on the fly when subscribing to a random website, without having to go into the admin settings. And naturally they should also offer wildcard sending (being able to send from [email protected] – this is supported by most decent email clients).
Bottom line, as long as it's your own domain and you don't abuse things like receiving/sending limits, attachment size, total storage size etc. you should be able to do whatever you want with your addresses and mailboxes.