Which Database is suitable for C# windowss application before deployement and also suitabale for client?

How can we decide what you should use? You should know what your needs are and then you should evaluate the product that best suites you.

We are not psychics; when you take the time to ask a carefully composed question and include enough specific information about the context (hardware, software, you, client, the current and future needs of the application/database), you'll get assistance.

You can use any repository including files on the file system. You need to describe your system in more details. I would suggest MS SQL server as most natural for MS development, but that depends on your target clientele (if they can afford the license).

If you're going the SQL route, it genuinely shouldn't matter. Just make sure you expose the capability to change the connection string, and if you're worried about customers not having an onsite database you can include SQL Express or Compact as part of an installer.