I don't believe it's ever correct to start dusting your commons and uncommons. The return is just too low to justify clicking three times just to get one or ten Shiftstone. Eventually, the "Destroy All" button will do that work for you!
When I first started playing, I destroyed ALL of my premium cards. Commons, Legendaries, and everything in between got put in the grinder (as long as I had a playset of regulars, of course.) While I do recommend doing the same for Legendaries (destroying a premium Legendary will get you enough stone to craft any Legendary of your choice,) I really wish I had saved all of those commons and uncommons. However, if you know for sure that you'll never care much for premiums, then go right ahead and collect that Shiftstone!
This list is divided into four groups. Rares from The Empty Throne, Legendaries from The Empty Throne, Rares from Omens of the Past, and Legendaries from Omens of the Past.
Now, some cards that may or may not be on this list may come as a surprise to a lot of people. For instance, where is Moment of Creation? I was careful not to include cards that I believe can or will become competitive in the future. Basically, this is a list of cards that are both 1) not currently good enough and 2) likely won't ever be good enough to be competitive. If playing fun decks is your jam and you aren't worried about building that next Tier 1 deck, then you might want to save some of these cards, such as Stonescar Excavator or Mind Link.
My next project will be about the cards you should prioritize crafting with all of this new Shiftstone you got from destroying all of these cards! Until that time, you can follow me on Twitch at https://www.twitch.tv/TheSkeeJay and I'd love to hear from you there!