A lot of online shops today uses MySQL!
What's more important than what database you use, is the level of security of your code! ALLWAYS run a scrip that makes sure that there is NO sql commands in any user input - like a search field!
Read more about security (both sql and php) in the php manual:
If you fail to make you database as secure as possible - any user can run a sql command and add them self as a user and mix up you database or delete them!