This kind of system isn't very difficult to program. A good language would be PHP.
You did not mention if you have any programming skills but if you do you should be able to program the system if you are willing to learn the basics of SQL (Structured Query Language. A rather simple language for doing queries on realtional databases)
To get started I'd recommend creating a MySQL database (can be done from the cPanel by just setting a databasename and username & password pair) and then heading to phpMyAdmin (also from cPanel).
PhpMyAdmin is full graphical web utility for managing your databases. You shold be able to use it with no problems.
First select your just created database (from the pull down menu at left) and then create some tables in it. A table structure for your album database could be somthing like this:
Albums table:
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album_id | artist_id | album_name | year | record_label
Artist table
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artist_id | artist_name | country |
The fields of course can be anything you want... But it is smart to have id's for all rows (and setting them to auto_increment) so that each album and artist has an unique ID.
After you have created the tables (you could create just one for testing) then add some data to them. This also can be very easily done from the phpMyAdmin. But pay attention to the SQL code that phpMyAdmin prints out. This is the form that your scripts should be using when they insert/get data to/from the database. After few inserts you should be able to get the idea how SQL works. It is really that simple. Then you could read more about SQL and MySQL DBMS (database management system) from
http://dev.mysql.com/doc.
Next step would be to create scripts to do queries from the database and printing out the data in a suitable manner for your site. I personally use PHP, but I'm sure ASP or JSP are just as good options for this. If you don't know any of these languages yet but have some previous programmign experience, pick the one that's closest to what you've been doing before. PHP is quite similar to C, if you know C you'll learn PHP real easy. JSP is Java for server side scripts so if you're java-man you'll feel home with JSP.
At least PHP has excellent online documentation (
http://www.php.net) with lot of examples. Also for dealing with databases.
I hope this helped. Dealing with databases is whole lot easier that you might think, but like everything new, it takes time to learn and get used to it. And if and when you ran into problems remember that these boards are filled with people willing and capable to help out.