I am new to programming and want to do a few apps for the small company I work for and need help on where to get started. I would like to host a database on the company’s domain that I purchased. An example of an app I want to program might be an inventory control program. I was hoping someone could point me in the right direction to get the database up and running and be able to update it from an android app.
To be honest, my advice would be Android programming forums. This article http://www.androidhive.info/2012/05/how-to-connect-android-with-php-mysql/ found easily from a web search looks very similar to your aim.
You can create the database in your DreamHost Panel, then use PHPMyaAdmin to manage the database.