Fastmail provides an easy way to migrate [0]. I setup a label in my Fastmail account that will tag all mail coming in from Gmail. Then you go through that list at your leisure and make the requisite contact with the people or services emailing at the old address. It's really not difficult at all. I've been on Fastmail for ~4 years now, and haven't once considered looking back or regretted it. Good luck.
[0] https://www.fastmail.com/features/migrate/