Getting back into PvE

I've recently geared up my Balance Druid from scratch (new level 90) to ilvl 510 in less than 3 days. I'll list the complete steps below in case it's useful to someone. You can jump to step 4 since you're already at ilvl 475:

1. Do scenario 'Arena of Annihilation' for the first time and get ilvl 450 weapon. (10-15 minutes)

2. Do random scenario and 5-man dungeons, each 1-2 times per day, to get ilvl 463 armors and collect Justice Points/Valor Points to weekly limit. (4-6 hours total)

3. If you have crafting profession for your class, you can craft the ilvl 476 PvP armors to fill those slots that you didn't get any 463 armors. If you don't, you can buy them on the AH, they're very cheap now as in patch 5.4.

4. Go to Timeless Isle, do the basic 'Talk to X' quests and open all chests within your reach along the way, you'll get at least 3-4 timeless ilvl 496 gears and some Timeless Coin. (<1 hour)

5. Buy a stack of Golden Glider and use them to grab the Blazing Chest which has a guaranteed loot of Burden of Eternity. (10-15 minutes)

6. Put on the timeless armors and use the Burden of Eternity to upgrade the slot that have the most itemization value to ilvl 535, which is Chest or Leggings. This will effectively raise your combat ability to do the quests on the isle.

7. Do dailies and random grinding on the Timeless Isle until you get 50 Lesser Charm of Good Fortune. If there are people attacking elite mobs you can hitchhike to get a chance of loot. Now you should have 10k+ timeless coins, go to the cave and gamble with all the coins. You'll get another at least 3-4 timeless gears from this process and if you're lucky you'll get 1-2 Burden of Eternity's. Again, apply the Burdens to the slots with high itemization value. (2-8 hours depending on your class, spec and gear)

8. Now your ilvl should be over 480. If not, go to the Valor Quartermaster in Niuzao Temple to buy some 489 JP gears. (Note the name is VP vendor but he sells JP gears.)

9. You can queue for Throne of Thunder LFR to get some ilvl 502 loots, as well as do daily Heroic Scenario run to get some ilvl 516 gears. (4-6 hours total)

10. Now your ilvl should be over 496. If not, since you're already Friendly with Shado-Pan (thanks to the ToT run), you can buy ilvl 522 VP gears (preferable necklace, then ring or trinket) from the Shado-Pan Quartermaster in Niuzao temple.

11. If you're still not 496 yet, you can either buy some 496 PvP gears with Honor Point from the Honor Quartermaster on Serpent's Spine, or continue grinding on Timeless Isle.

12. Once your ilvl hits 496, queue for Siege of Orgrimmar LFR. Don't forget to turn in the Lesser Charm of Good Fortune's for Warforged Seals before you enter the raid. Use Wowhead, Atlasloot or AskMrRobot to find out which boss drops the best loot for you and you may want to use the bonus roll.

Good luck!

Here's a quick cheat sheet for ilevel rewards in 5.4:

ilevel 496 - all slots except mainhand/offhand,
  Timeless Isle short grind (chests/rares),
  1-2 days
ilevel 496 - mainhand,
  Timeless Isle medium grind (20k timeless coins),
  less than a week
ilevel 535 - all slots except mainhand/offhand/trinkets,
  Timeless Isle long grind.  (Burden of Eternity),
  random, but no more than 5 weeks

ilevel 476 - Mogu'shan Vaults LFR
ilevel 483 - HoF and ToES LFR
ilevel 502 - Throne of Thunder LFR
ilevel 528 - Seige of Orgrimmar LFR
ilevel 540 - Seige of Orgrimmar Flex

All of these items may be upgraded for valor to get +8 item levels.

Also, check the auction house for crafted gear.