4. Gradually move things over to the new address as you notice things which still use the old one, possibly over the course of years.
Eventually you will run out of reasons to keep your gmail account and you can just close it. I migrated from gmail using this approach and it was not difficult in the least.
5. Make really, REALLY sure that no important thing is still set to the old address.
At $Work, we received a domain registrar password reset e-mail today - for a former client who I don't think we've talked to in 15+ years. Banks, registrars, etc. seem to store stuff like e-mail addresses in more different fields, in more different databases, than any 3+ of their customer service rep's can find & fix right.
Well, you may encounter one or two issues in the years following the shutting-off of your gmail account. But what would you prefer: one or two issues, once in a blue moon, which can probably be solved by a semi-competent customer service team on the other end; or having all of your Google services shut down without notice and without any recourse whatsoever?
2. Set up auto forwarding
3. Done