I want to find out what options I have regarding storing my data securely in a mysql database.
Can I store the data so that it is encrypted?
Can I store the data so that it is scrambled so if someone managed to hack into the database, it would not make much sense to them?
Yes, mysql has encryption built in to later versions.
You should begin by reading the Security section of the manual.
See this thread for a variety of opinions on the subject.
Spoiler: my view is that encrypting data in a database (certainly at application-level) is counter-productive.
Mark