I would like to know what the difference is between the different "grades" of guns. What is the best grade and which is the "non-premium?"

When it comes to grade most manufactuors star with a basic shotgun. The step up occurs when a better piece or wood or more engraving.
An easy example would be a Browning Citori in Lightning configuration.
Grade I is standard
A Gran Lightning is the same except for an upgrade in wood.
Grade III is an upgrade in both wood and now you have more engraving
Grade VI is better wood and engraving with gold inlays.

This is the same for all makers

Think of them like options on a new vehicle. Some are prettier and some are funtional. Wal Mart can not walk you through the options. Try a reputable gun dealer and the price will increase with the options.