Trinkets aside because they're hard to quantify, though I'd put them as the highest Priority alongside weapons; depending on specific gear/how close you are to BiS, the order can be judged via the spreadsheet on which items generate the highest score calculated via the stat weights. Stat Weights are averaged out for the purpose of the sheet but generally our MH and OH stat weights are very similar, unless the Class Trinket is in effect which only serves to push MH WDPS even higher, so they are always top priority.
For example, if you take the Single Target BiS list as an assumed gearset, upgrade order based on tangible stat value would be:
Weapons >>> Chest > Head > Legs > Gloves > Belt > Boots > Shoulders > Neck > Ring > Wrist > Cloak
Obviously, this is different for everyone and depends on gear you're wearing right now, so you'd have to use the sheet as a tool to judge. I have a separate sheet with the upgrades to make comparisons of value pre and post upgrades that will be subbed into the sheet come patch day.
I'd advise if you're using gear under Mythic level and want to see the comparisons, to use the more robust sheet that Binkenstein put together that has comparisons of Normal -> Heroic -> Mythic values