Developing your DB on your local machine could be a challenge.
If you're new to all this, I'd recommend finding a webhost that will allow you to create a database (I also prefer MySQL) through their CP. (
pair.com comes to mind).
Once you have your DB, find a GUI client that can interact with it (phpmyadmin - if you plan on developing in PHP), or navicat (not free, but there's a trial) are great tools. PHPmyAdmin can be a bit confusing to the inexperienced, but it is free.
Learning how to interact with mysql from the command line will come with time.
Best of luck.