One thing I will say, especially during Realm Reborn, new players often feel like skipping through story bits because it feels like it's taking too long. The first expansion (Heavensward) is where the story really picks up. Even so, don't skip the cinematics. And don't worry about watching cinematics during multi-player bits either. The community is known for being very patient with sprouts watching cinematics they haven't seen before. Neigh, as a matter of fact, they will downright plead with new players to not skip the cinematics.
And if you ever run into trouble, don't be afraid to ask, here but even in the game. The FF XIV community is pretty well known for being friendly to newbies.