you don't need mySQL to run PHP. however, for a catalog site like you're referring to, it is definitely an advantage to have all your inventory and links stored in the database to speed up the process of the page, but PHP and MySQL are two entirely different tools. as for the website and database question, almost all larger websites in some respects are database driven... at least in part. keeping track of content, memberships, files, etc. are all reasons to learn to use a database when working with webpages.
your best bet to create your tables would be to check into an application similar to phpMyAdmin or other that would give you the GUI interface to start with. eventually, you'll be able to create your tables manually using only SQL statements.
hope this helps clear up some of your understanding.