Typically you would want to use an EBS backed instance. Since the free tier does not support that, but does offer EBS storage, create your database on an EBS partition for data you cannot lose
30 GB of Amazon Elastic Block Storage, plus 2 million I/Os and 1 GB of snapshot storage*
You should have a means to quickly launch a new instance, and you should back up the data on your EBS partition because EBS volumes can and do fail from time to time.
UPDATE
It seems that Micro instances are in fact EBS backed.
It is still advisable to attach a separate EBS volume, because it makes it much more convenient to backup the database (you create a snapshot of the EBS volume... you can find scripts online to accomplish that, which vary a bit depending on your choice of database and file system).