Good Luck moving your site.  You new hosting company will probably give you the server's IP or domain name,  You will need to create the database and database user.   If you are having a hard time with this, then I would strongly suggest hiring someone to help or move to a different hosting company that understands DotNetNuke (for example: PowerDNN, DotNetPark, DNN4Less ... )

AS for Drupal ... never heard of it 

Seriously, I have worked with Microsoft software since 1990 and found DotNetNuke to be a great fit for both my needs and skill set.  Luckly, the core team has managed the framework well looking both forward and backwards - moving ahead, but remembering the product's roots. 

Just to point out some easily overlooked points about a web.config file in case you are not familiar with it.

It is nothing more than an XML file that is has configuration settings specified in defined sections of the file.
The connection strings will be in the section named <connectionStrings>.

If your existing site used a mdf database that physically resided in the App_Data directory of your DNN site, it should have a connection string that resembles this:
<add name="SiteSqlServer" connectionString="Data Source=.\SQLExpress;AttachDbFilename=|DataDirectory|Database.mdf;Integrated Security=True;User Instance=True" providerName="System.Data.SqlClient" />

If your existing site used a database that was ran from SQL Server 2005/2008, it should have a connection string that resembles one of these:
<add name="SiteSqlServer" connectionString="Server=SERVER.HOST.COM;Database=DotNetNuke;uid=USERID;pwd=PASSWORD;" providerName="System.Data.SqlClient" />
    <add name="SiteSqlServer" connectionString="Data Source=SERVER.HOST.COM; User Id=USERID; Password=PASSWORD; Initial Catalog=DotNetNuke; providerName="System.Data.SqlClient"/>