Well, choosing about database is purely depend up on your size of the application and architecture of the application.
Size of the application
Medium or Large Scale Data
I suppose your application will not have very large scale data. If your application will have medium or large scale data, then I recommend to use SQL Server. If your concern is about licensing cost you can use SQL Express. Visit this http://www.microsoft.com/downloads/details.aspx?familyid=220549b5-0b07-4448-8848-dcc397514b41&displaylang=enfor more details and downloading it.
To develop your application in .net to use SQL Server database you can use System.Data.SqlClient library.
MS Access is also fine to use if your application is having small scale database. You can use MS Access as a database in .NET using System.Data.Oledb. You can create a DSN pointing your MS Access file and connect to it.
Another option is to use file as database probably XML is the best for this. But this is okay if your application has very few data manipulation.
Architecture of the application:
If your application is standalone application, you don't have option not to save database on the client machine. Because there would be only one machine where your application would be installed. Whatever database you use you will save the data on local machine
If you have many clients and one database, you need to make a database server. And from the client application, you will connect to the database for data manipulation. In this case I would suggest you to use SQL Server.
You can connect to the server using connection string. Connection string contains the details of the database such as database server address, credentials to connect etc.
I hope this helps to you. If not please revert back.