Ah! Ok, that helps a lot. It actually looks like a straightforward modification of osCommerce, so you should not have any trouble getting it running.
As for the SSL stuff, you can get guidance on that from the DreamHost wiki:
As for the MySQL stuff, DreamHost makes the creation of a MySQL database (for use with the sheebastore osCommerce template package) very easy. You can create if from the web panel -> Goodies -> Manage MySQL screens. Once you have done that, you can take the information from there to include in the configuration section of the store.
Well, you never can tell, but you might want to know that DreamHost abandoned the previously existing “one-click” installation of osCommerce in favor of ZenCart a while back. Maybe someone has cobbled (or can cobble) together a similar template for ZenCart.
Good luck with your project!