I had trouble finding a ready reference to the ilvl ranges for Mists, so after hunting around all the usual sites came up with the following. I’ll revise this post if the numbers change.

Update 2012.10.03: Revised Heroic iLvl (was i440), JP iLvl (was i450), JP/VP rep requirements (no rep for JP gear, less for some VP gear), and added crafted weapons iLvl.

Source Requires Drops Comment
Quests n/a i372
Dungeons i358 i425-i45
Scenarios i425 i463
Heroics i435 i463/i476 i476 final boss only
LFR i463 i476/i483 T14 tokens i483
Raid (N) i476 i489/i496 T14 tokens i496
Raid (H) i489 i502/i509 T14 tokens i509

So progression is pretty clear: Dungeons -> Heroics -> (LFR) -> Raid Normal -> etc.

You can skip LFR by grinding out enough rep and VP to get into norlmal raiding. Rep vendors sell i458 gear for JP (no rep required), and i489 for VP at Honored (neck/ring/cloak/bracers) and Revered.

So planning your reputation priorities will be important. Crafted epics are i476-i496. Crafted weapons are i463.