I'm on my phone atm so I hope this all comes out right. What I do is use Wowhead and search with whatever class it is your after. For instance say ur after a leather mog for aMonk, try this out :-
Then right near the bottom of all the mogs u have quest Mogs and BoE mogs. Now BoE is obviously level locked for ur toons but 20-29's can mog all the Vanilla questing sets.
That's how I go through the mogs. Weapons u will have to do a separate search. I sort items in Wowhead by ilvl and then look at the Vanilla ones that don't have. Level requirement. For instance the shield on my Warrior requires lvl 21 if u get the BoE but I found a quest in one of the Plaguelands that awarded the same shield without the level requirement.