Do I still need to install SQL Server Express engine (A win Service)
on client machines?
Yes, they need it installed for your application to query the database. Can't really get around it.
There is a flavor called SQL Express localDb. That one does not need
an engine (win service)? but I think it need a perquisite installation
of localdb.
Yes, you'd still need to install LocalDB on the client machine. It's pretty hassle-free to do, but I think it's overkill unless you really need the full features of a SQL Server instance for your webservice.
Instead of LocalDB I'd strongly recommend using SQL Server Compact Edition - it performs the role you're thinking of (your WCF Service can simply connect directly to the database file on your client machines without installing SQL Server, and is lightweight), but doesn't need to be installed (it's simply included as a DLL with your WCF application):
Unlike other editions of Microsoft SQL Server, SQL CE runs
in-process with the application which is hosting it.
In Microsoft's own words on the differences between LocalDB and SQLCE:
LocalDB and SQL Server Compact?
Small and simple database, lightweight installation, connecting to a
database file -- this will sound familiar to any developer using SQL
Server Compact. The similarities are not accidental, as our goal for
LocalDB was to be as easy to use as SQL Server Compact (while being as
powerful and compatible with full SQL Server as SQL Express).
There are significant differences between LocalDB and SQL Server
Compact:
Execution mode: SQL Server Compact is an in-proc DLL, while LocalDB runs as a separate process.
SQL Server CE is kind of like an updated version of MS Access, the file goes with the application which can "just connect" to the database file without involving any database server installation, and its syntax/features are very close to SQL Server standard.