I am trying to learn how to make a mobile phone communicate with a server and a database.

So far, I have made a web-service on my PC using this tutorial: http://msdn.microsoft.com/en-us/library/ms733069.aspx

The above tutorial makes a sortof WCF service. What would be the best Database system for me? Simplicity and ease-of-use is key.

I was thinking either RavenDB or SQL Server.

Any suggestions on what I should use and if there are any digestable tutorials online?

I'm not to famliar with RavenDB but SQL express or MySQL are easy to install. There are plenty of online tutorials for using either one and the basics of SQL (table creation, inserting and retrieving) aren't hard to learn. The MySql dev site can help you with most queries.

What would be the best Database system for me?

That is a very subjective question.
The answer is probably: The one you've used before, if any.
If you have never used a database before and you're approaching this a a user, the brand probably won't matter.
If you're doing this as a DBA, you'll just need to pick one and DIG IN.
There is already a lot of support for the the ones mentioned by hericles. If you do this for a company, they'll probably expect you to know SQL Server or Oracle.