how do I get a @me email and be able to update my account to use the new email account?

You cannot create @me.com addresses. Any email aliases you create can only be @icloud.com. If your main iCloud address has the @me.com version because you were a member of MobileMe that will continue to work and will deliver into the inbox, so you dono't have to do anything to receive these messages. If you started with iCloud (so later than 2012) you won't have this and you can't get one.

I don't know where the page linked to above got the idea you could create @me.com aliases, unless it's an old one that hasn't been updated for ages. This is Apple's page on creating aliases:

https://help.apple.com/icloud/#mm6b1a490a

Messages to an email alias address go to the inbox alonside messages to the main address, so you don't have to take any action to receive them. You can choose such an address as the 'From' address when sending. You should be aware that email aliases cannot be moved to another account, turned into an Apple ID, used as a login, or retrieved if deleted.

Try https://www.groovypost.com/howto/apple-icloud-create-me-com-email-alias/

Once you create the alias, it should appear in your account under Reachable At. You can then start using it in Mail.

Apple ID - Manage