There really is not a simple database, the designs of the database and the features of the database environment used determine the complexity. But let's say you do have a simple page with minimal database requirments then a simple website + database would = SIMPLE.
Wordpress is simple for a BLOG or a simple static 'looking' type of site, but not as simple if you need to implement explicit database behaviour that does not come standard in your Wordpress template.
If you need a single page that connects to a database then you probably have a front-end site composed in HTML and CSS with your database logic handled by a dynamic language like PHP or ASP.NET. These would connect, push, and pull data from your database. As far as database choices, popular free databases are MySQL, Postgre, and SQL lite.
Steps might be
[*]Find host that has your script and database environment working, let's say PHP and MySQL. You want to understand what data limits you may have as some hosting packages can be quite restrictive in the amount of data and the number of databases that you are allowed in your hosting package.
[*]Install a LAMP or WAMP stack on your local computer that will simulate the environment on your host. This way you can code and test locally.
[*]Design or Import your database into you WAMP/LAMP MySQL database.
[*]Use PHP to make a connection to your database, for this you can use MSQLi or PDO as a driver/layer for your database connection and queries.
[*]Integrate your php page (that has the database queries in it) into a my_page.php and start dressing it up using markup and CSS.
[*]When complete upload your my_page.php to your web host and you have to export your database (at least the structure, you may not want the test data) and then import it into your web hosts database. Typically your web host will have a control panel that includes PHPMyAdmin for doing this. So you would export you Db using PHPMyAdmin in your WAMP/LAMP stack and then import it using PHPMyAdmin on your host.
Often people just focus on front-end design HTML/CSS/JS and other people do back-end design PHP/ASP.NET/JAVA and even other people just specialize in Database design and management. That should tell you that there is a lot to learn and is probably like learning front-end design all over.