It's fairly easy to get gear these days, the best way would be to go straight to Timeless Isle, your item level should be a bit too low so you wont be able to bot / farm very efficiently but if you do all the intro quests and just walk around and tap some rare mobs you should get loads of Timeless Isle armour pieces quite fast and suddenly you have all 496 gear besides your weapon and one trinket. It doesn't take very long for you to get a Burden of Eternity by doing the quests and that's a 535 armour piece, and you also have the opportunity to attack a albatross and fly towards the chest which gives you another Burden of Eternity so that's a second 535 right there.
If you are lucky you might get one from the rare mobs if you decide to stay and farm for a bit. Then your gear is more than good enough to start running some LFRs, from Siege of Orgrimmar you might get some item level 516+ gear and you also have the new Iron Invasion questline in Blasted lands which gives you decent bracers, neck and one trinket.
Doing the Iron Invasion, farming Timeless Isle and using DungeonBuddy for Siege of Orgrimmar should give you item level of 505+ so you can do the new UBRS which gives you 4x 550 pieces.. Then you are pretty much good to go for the expansion, if you manage to get yourselves 10k gold you could also pay for a Siege of Orgrimmar Heroic boost so you get the weapon heirloom from Garrosh.