New C# accounting application - what database to you for application file?

Question

Good evening all,
I am developing an new application that will use a double ended book-keeping accounting database, based on a prototype that I have developed with MS Access.
My question is as follows:
What options do I have available to in order to generate application files for users that will store multiple relational database tables and data, and still be able to employ SQL expressions? The requirement is that the dependencies must be free, and able to be installed with my software, using an installer program. What can anyone recommend me?
To those who want more backgroun information:
My project is at the moment an MS Access database, but I want to make it a C# application for the following reasons:
1. Faster performance - my program will only focus on functionality that is necessary;
2. Portable - my program can installed on any Windows XP/Vista machine;
3. Advanced features that are not possible with MS Access.
Thankyou to all that reply.