correct database for c# window application?

I am going to develop a window based application using c# 4.0. It is a database driven application, i.e it is going to have some manipulating the records of students and other stuffs.

I use to work basically on web platform, but on this project, I have to use c# window forms. 

So those were my scenario, now come back to my question. I am confuse to selecting the right database. I am very comfortable with SQL Server. but can i use that in my window based application? I mean, after completing my project, I have to deploy the software, and make an exe file, which would be running on any computer. What i dont want is that, the user who would be using the software, should not be aware of the running database. If i use SQL server with my window app, so at the time of installation to user computer, will I need to install the SQL server on that system too? Or I can include some basic dlls in my project at the time of deployment? so the user just need to install that exe or setup file of my project, and every thing functional..

I think I was able to express my questions.

Please, need some urgent advise on it.

Thanx