Deploy MySQL Server + DB with .Net application
Not sure where you're at in the project, but if it's a simple and small database you might consider converting it to SQLite. It's not ideal for Client/Server operations, but if it's low volume/transactions it might work.
Use an installer with a worked out script. Any installer like Wise, InstallShield, InnoSetup, etc will probably do.
We took a different approach on this. We make MySQL xcopy-able, by writting a wrapper to generate the configuration file(my.ini) before calling MySQL (to correctly setup the base path and so on). Then we written another service installed using the standard setup. This service will take care of starting MySQL and other required background program (in our case Apache) for us. Since the MySQL is deploy by us, we wanted to have full control over it.