I'm now going to learn .NET Remoting and have a plan to modify my
application to use Remoting, but what's the advantage of Remoting? Is there
any perfomance benefit if I use .NET Remoting?

I don't know the exact specifications of your project. So i can't tell you
for sure what is the best for you. However, it seems to me that a web
service approach would be the best for you here. As i understand, a client
application on the user's PC is, in the current configuration, accessing the
Database directly. This forces you to implement Database access and
retrieving/formatting of data from the database in the client itself. If the
database design or location has to change, you'll have to modify the client
and redeploy it. Furthermore, you have no way to use the client on the
internet as it would pose major problems and security risks.

Now, if you create a Web Service that offers functions such as 'int
NumberOfItemsLeft(string itemName)' for example (i don't know what your
application is supposed to do, so i'm picking up a typical example). The
client application will just have to call this Web service function to have
the number of items left for a particular item. This is straitforward to do
on the client.  The web service will access the Dabase, retrieve the info
and pass it back to the client. If the database is redesigned and moved
somewhere else, you'll just have to modify the Web Service while the client
application will keep working as usual without noticing anything. And you'll
be even able to use the client from the Internet, adding more security such
as SSL encryption if needed.