SQL Express is free and I believe supports databases up to 4GB which should be ample.
MySql is also a good choice, this site runs on MySql, so MySql is the most tested data layer we have after MS SQL. PostgreSql is also very robust and free.
any of the open source databases or even MS SQL Express can be used for commercial purposes. With open source licenses the issues are typically not about how you may use them but how the software may be redistributed. If you are not re-distributing or modifying the source code of the database software you are not likely to violate the license.