Connection string for connecting the SQLSERVER Express Database and just how to consider setup of this database with my application.....

The next snippet should enable you to get began .

SQLConnectionStringBuilder bldr = new SQLConnectionStringBuilder        
    bldr.DataSource = "Server"  //Put your server or server\instance name here.  Likely YourComputerName\SQLExpress        
    bldr.InitialCatalog = "MyDB"  //The database on the server that you want to connect to.        
    bldr.UserID = "SomeUser" //The user id        
    bldr.Password = "SomePassword"  //The pwd for said user account
SQLConnection myConnection = new SQLConnection(bldr.ConnectionString)