The old raids have the ability to be synced-forcing you to run them at the level intended; however, they also have the ability to run them unsynced so they can be cleared as the cap. Old raids will usually be done unsynced, since few want to plunge through progression with old content when they're overgeared at their cap anyway.
Running old content, however, does happen. There is a book WT/Wondrous Tales (weekly quest) that has you run through various content, PF or FC is a good way to get small groups for it (as unsynced doesn't really need full parties on most things). There is also what the FC calls "Bridge Night"-- This is when people help clear older/less current content for other--unsynced is normal but synced stuff too. While the night hasn't had a specific time of when the FC runs it; if you ask and there is enough people on that are able/not raiding at the time, it usually happens. If not, most will try to help you out soon as they can.
As to Focus on story before raiding. the SB raid will likely be gated behind the completion of the 4.0 storyline; as I know ARR's was and think HW was. So clearing story asap will help a great deal and start preparing you for raiding.
if you've more questions ask me on this topic or on discord; will do what I can to answer