Fastmail does the email migration in the cloud. It’s relatively quick and painless, and you can trial things for a period by setting up your gmail account as an alias (send from the fastmail web interface through gmail’s smtp servers etc) so you can always switch back if you don’t like it. When satisfied, set up an auto-responder and forwarding to let people know to stop emailing your @gmail account.

Fastmail has a decent calendar, but you may prefer to use iCloud or something else for that. Calendar clients on desktops and phones tend to be pretty good at supporting multiple providers so that is a lot easier to migrate.