Hello to the well knowledgable out there,

I have just began the book from Sitepoint "Database Driven Websites - using PHP and MySQL" and have a few questions (I would like to add that I am not sure if I am accurately asking these questions -- please bear with me):

The situation:
I am instructed to access MySQL and use PHP script; the options pointed out in the book is:
1.) If my host offers MySQL and PHP then I can access what I need from the host.
2.) If they are not offered then download them to my machine.

The situation I face is that my host offers an empty database for my use at a cost to me. Of course I wanna go free!

The questions:
1.) Concerning the needs of the book: Is a database just a part of what I will need to access from my host; in other words can I access other needed parts of MySQL from my host, apart from the database (thus creating my own database down the road)?
2.) If the database is integral to the requirements of the book and essential to have, what are my options? a.) partial use of MySQL from the host and create my own database? b.) download everything I need from My SQL's site and run from my computer? c.) other options d.) do you understand my question?

Note: I am just a beginning and I know only what the first few chapters speak about.