What I would suggest is to start out by doing the Normal Mode raids this tier through the Duty Finder, because the savage versions (which are what 99% of statics are going to focus on) build heavily on those mechanics.
Beyond that, make sure to practice your main job, I would suggest choosing just one, and really dial things in so you're super comfortable on it, as that will help when you're also having to do mechanics on top of keeping your damage up.
If you're going to play Dark Knight, it's also important for you to learn how to do a Tank Swap before you start doing Extreme or Savage content, there are many videos on the internet that will teach you how

The normal mode raids are designed to be very accessible to newer players, and they don't punish you nearly as hard as savage; you can get through them just fine as long as you're paying a little attention, no videos or guides really required. You'll probably die to mechanics a couple times, but people are generally very forgiving of that kind of thing.
Regarding story, there's minimal story you'll miss if you don't do savage, and the only story you'll miss at all is from the very last floor of Eden Savage.