
Based upon the official upgrade docs here you cannot do an inplace upgrade. Honestly that would be the bad idea anyway. If anything goes wrong during the upgrade process (or things don't work when you're done) you have lost your SharePoint site. You should bring up a new environment for SP 2016 and migrate your existing databases over. If anything goes wrong you can reset and try again. Meanwhile your users can continue using the old SP site. Once you've verified everything is working you can have everyone switch to the new system (or ideally just change your DNS entries to point to the new servers).
As for stuff changing while you are testing you can either specify a blackout date during which any changes made in SP will be lost or you can blow away your databases, lock down your old SP system and then backup/restore your databases a final time. Depends upon your needs.
As discussed here you cannot upgrade from SP 2013 to a version of SP beyond 2016. To get to the newest version you'll need to upgrade multiple times. Note however that you could spin up a SP 2016 instance, migrate your SP 2013 site and then upgrade again. If you want to break this up over several months then you can migrate users to 2016 as you go but it might just be easier to have them wait until you get to 2019.