Hello Dave
The factory reset will erase all content and settings, so assuming you’ve backed everything up either in iTunes on the PC, MaC, or iCloud, and dropped it into the new phone, you’re done.
iTunes accounts aren’t really a thing anymore, I’ve been through a lot of iPhones and only used an iTunes account on my PC for the iPhone 4. On your new phone you can hit Settings and see your Apple ID up top, look in there and scroll down to see devices associated with it. If the old phone is in there, click on it and remove from account. Password required.