In my opinion all that you need is a new mail provider/host of your choice and an own domain if you want to make future moving of mail providers easier.
Hosting an own mail server should not be your main focus when making an initial switch away from Gmail.
In your case Google would be the host/provider of your Gmail e-mail service and gmail.com is the domain name of the Gmail e-mail service.
Having your own domain name would allow you to keep you e-mail address even when switching your e-mail host. Which means you would not have to bother with re-registering you new e-mail address for every service or newsletter again.
yourname@yourdomain.com would always be yours no matter which e-mail provider you choose, IF they support a personal domain.