Installation showing only SQLite as database option
You won't be able to convert an existing site as far as I know; you'll need to build a new site and migrate the content over to it. It might be easier to just start a new site from scratch and export/import the data manually, depending on how far you've got. 

Before you do that, you need to enable MySQL in PHP. If you only see SQLite as a DB option, it means you haven't installed the PDO MySQL extension. Consult your web server's documentation for instructions on how to do that.

Once you have, MySQL will appear as an option for installation.