Teir 1 chests include leather armor, wood swords and axes, stone swords and axes, flint and steel,fishing rods,sticks, iron ingots, gold ingots, low saturation foods (melons, cookies,fish) decent foods(bread,pumpkin pie,carrots,apples) they can also contain stuff to craft arrows and probably other stuff I'm forgetting.
Teir 2 chests include gold,chain and iron armor with stone swords. You also will find boats, and good saturation foods (steack,pork,soup), flint and steel, golden apples and diamonds.
Its also a good idea to know where some of the tier 2 chests in a map and form a chest routes, chest routes are when you go the same direction every time you play a map to grab some chests you know will have some good stuff.
I hope this helped and that tier1s and 2s will be easier to figure out!