Raid gear is a reward for raiding and is good for gearing up to a high level fast with the highest level equipment while you get equipment with tomes. (Tomes (tomestones) are tokens you receive primarily for doing instances and can be exchanged for high level items.) This gear is not really necessary to catch up on the story at all, and once the expansion comes out in 10 days, it'll be quickly outdated anyway.
To jump right into the expansion you don't really need to do anything special with your gear, as the item level requirement for dungeons and story-based instances has always been low compared to the highest item level. For example, the last story-based instance required your character's item level average to be 90, while the highest possible average is currently 130. You'd be able to get to 90 easily by doing dungeons, the Crystal Tower raids (which are a bit more like 24-man dungeons), and getting tome items. In fact, if you make friends with a generous crafter, it's possible to hit this requirement with crafted gear alone.
Yeah, it's a direct continuation.
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Edit: Screenshot time! Got my Apocalypse, the last ever Zodiac I'll do, honest.
Veil of Wiyu Nexus, which I had for slightly under a minute, until...
Bye bye, dorky reading light.