The second sentence in your question has a faulty assumption, which means you are trying to solve a problem that doesn't really exist. There is no need to worry about "keeping the servers in sync".
You can shut down the servers in your farm in any order (and bring them back up in any order). You don't even need to worry about stopping individual services - just shut down the system. The worst that will happen is that you will get a lot of errors in your ULS and Event logs (if, for example the WFE comes up before the database).
The absolute cleanest way to do it would be in the following order:
- Application servers
- Database servers
and then bring the servers back up in the reverse order.
When Forms Services (and possibly Excel services...I've seen conflicting documentation) are in use, they sometimes have sessions that go through multiple HTTP requests before committing a transaction to the database - this is where the quiesce farm command comes in. It allows session(s) to finish doing one of these multiple request transactions, but doesn't allow any new sessions. After all transactions are committed the Infopath (Excel?) services are offline and ready to be shut down as well.
Here is a blog post that goes into a little detail about what Quiesce farm is doing:
You didn't talk about the end user experience part of this equation at all, but I will mention it for completeness. If you were to shut down a WFE in the middle of a user uploading a file or editing a list item - there wouldn't be any corruption of the WFE or database, but the end user is basically just dumped to an error page that doesn't really let them know what happened (or if there edit happened!). The way to deal with this would be to have something in front of SharePoint (a load balancer, even ARR on a separate server could do this) that would gracefully "drain" SharePoint of end user connections, and potentially redirect to a friendly error page until the site is back up.