Speaking for myself who recently made this change, it can take some time and be a bit complicated, but any decent mail provider that you choose can receive messages from external providers. In my case, I use Fastmail with a custom domain and receive messages from my Gmail account as well.

Just keep in mind that you don't need to change every single account at once. You just need to change the ones that you use the most, and with time you can change the others that you remember.