maintaince of the project from client side

Create a "Setup and Deployment" Project, which will install the app and required files (including the .NET framework) for you.

You should not attempt to install SQL Server (Express or otherwise) at all:

1) They may already have SQL Server installed on the network. If so, then they will presumably want to use that version.
2) If they do have SQL server installed and you start proliferating SQL server Express instances, you are going to annoy the heck out of the database administrator...
3) A single site installation of SQl Server is a lot more likely to be backed up than a number of scattered version under user control.
4) Sql server is quite complex for a "normal" user to install and administer - it is not a good idea!
5) It will destroy the primary advantage of using Sql Server over SqlCE or SQLite - multiuser access. If everyone installs their own copy of SQL server, then you will have multiple copies of your database, each used by a single person. This will cause some confusion, and (depending on how you wrote the original database) may take some considerable effort to combine into a single instance when the problem is realized.

Instead, provide a link to SQL Server Express, and explain to the user what they need to do.