I'm developing winform application(.net) which using database at very minor level. Some very basic structure of tables.
I've created windows installer project(.msi,.exe). I know how to put .net framework with this installer, so when user try to install my software and his/her system doesn't have .net framework, that can be install using same msi.
Now my situation is I need to install sql server(express edition) engine to client machine while they install my software. I don't want to install SSMS(sql server management studio-IDE) to client machine.
SQL Server can be installed unattended - all you do is redistribute the single installer file for the desired edition, then invoke it with the correct parameters. Keep in mind that this is not trivial, and cannot be done as part of your initial installer. There is plenty that can go wrong as part of this install, so you either need to handle it somehow, or spend a considerable amount of time supporting your installs. AFAIK there is also no way to reliably roll this into a merge module so that you could make it part of an MSI.
If you only want to use basic structures in a small database, consider using one of the LocalDB editions of SQL Server instead.