The key here is which database you need. Is this database accessible to multiple users of the application? If so, then MySQL will be fine.
But it looks like you are going to use this database as a private data warehouse, where each installed application instance has its own local data for this computer or profile. In this case, you need a built-in engine such as Sql Server Compact Edition, Sqlite or even Access, and not a server engine like MySql or Sql Server Express Edition.
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