It's not really a case of proper order of shutdown as much as properly shutting down.
In theory, you'll want to stop or allow to complete any email fetching that is ongoing, and stop all cron jobs, and OTRS scheduler, then apache, then MySQL (if you really must stop MySQL or apache).
It's a web app, so much of what is happening happens within a few seconds, as transactions to the SQL database and web lookups. Since MySQL is the most important part of the data equation, but doesn't *generally* need to ever shut down, aside from upgrades/reboot, you'll simply find that the app won't work if mysql and apache aren't working, and apache may not work (well) if mysql isn't working/on. The OTRS scheduler and scripts are not constantly running, so they can be stopped or started at whim, and they themselves don't stop or start their components when they are reloaded. (That is, a mail fetch will happen as scheduled and will continue to finish, if it's already started, even if the cron job is deleted. The mail fetch won't happen again until the cron job's criteria is met.)