This is not a complete answer for you but may give you some things to think about.
First you might want to think about your choice of database. If you don't have a compelling reason for using 2005 you will probably at least want to move to SQL Express 2008.
Second, to answer the part about creating a server... A server is something that serves data. In a general sense a computer configured to be contacted by external machines and respond with data is a server. A web server runs a program like IIS or Apache to respond with web pages. A database server contains a database and allows connections to that database. So as long as you install the database on a computer and configure it to allow external connections, you have your database server.
In MS SQL there are several things that need to be set up to allow a database to accept external connections. One is that the SQL Server Browser service will need to be active. Another is that the database itself will need to be configured to allow external connections (SQL Authentication type probably).
Hope this helps.
Addition:
SQL Remote Connection Configuration
Disclaimer, I don't have SQL Express 2005 installed but I think the settings are found in the same place in 2008. If the info here is not exact to SQL Express 2005, the general terminology used here should be enough to get you headed in the right direction to find the specifics.
While viewing the database in Server Management Studio or Enterprise Manager, right click the database server instance name (the root of the tree) and select properties. There should be a section title Connections and within this section there should be an option "Allow remote connections to this server". Make sure it is checked. The other setting you need in this properties menu is under the security area. There is a radio button for "Windows Authentication Mode" and "SQL Server and Windows Authentication Mode", you want the second that allows both.
The next step you have may be to create a new user, add a password, and connect the user to the database. That will give you the credentials you will use in your database connection string while programming. I usually add new users through the security section of the database then set the User Roles for each database that I need to connect to. It is good practice to limit the permissions to those needed by the application. Typically this is read and write, but sometimes you can get away with just read. The less the better.