1) The hosting compnay Dreamhost provides it. I can add unlimited MySQL database on it.

2) This Blog named as What A Lamp. The m of it stands for MySQL.

3) The other reasons I posted below are copied from MySQL official site. You can just treat it as an advertisement.

The MySQL® database has become the world’s most popular open source database because of its consistent fast performance, high reliability and ease of use. It’s used on every continent — Yes, even Antarctica! — by individual Web developers as well as many of the world’s largest and fastest-growing organizations to save time and money powering their high-volume Web sites, business-critical systems and packaged software — including industry leaders such as Yahoo!, Alcatel-Lucent, Google, Nokia, YouTube, and Zappos.com.

Not only is MySQL the world’s most popular open source database, it’s also become the database of choice for a new generation of applications built on the LAMP stack (Linux, Apache, MySQL, PHP / Perl / Python.) MySQL runs on more than 20 platforms including Linux, Windows, OS/X, HP-UX, AIX, Netware, giving you the kind of flexibility that puts you in control.

Whether you’re new to database technology or an experienced developer or DBA, MySQL offers a comprehensive range of certified software, support, training and consulting to make you successful.