Since we moved from XAMPP to IIS7 we've had one downtime, and that was for mistaken data deletion. Moodle itself has been absolutely rock-solid.
The backup of MySQL & the moodle data was exactly what we did, keeping the MySQL instead of moving to MSSQL - we were already in a disaster situation with crashes and figured moving to IIS and MSSQL at once was probably a bad idea as it could have introduced other issues that we'd never be sure of the cause.
It was surprisingly simple to do. We took our usual backups, performed a second backup with a different app, and moved everything over and tested within an eight-hour window. The main difference the users noticed when we completed the migration was the site no longer crashed.
Be sure to bring any additional (read: non-default) blocks over as well. We neglected this part and it caused a bit of indigestion among the staff post-recovery.
I'd also recommend spinning up a new server (virtual or otherwise) for the move. That way, you always can go back to the original if the whole thing goes pear-shaped.
I have to give a hand to the IRC channels #mysql and #moodle on Freenode as well - they helped more than they realize for this n00b.
Deep breaths, go slow and be sure to stop for lunch if need be.