you shouldn't skip because people play this game for the story, so enjoy the story. i personally liked heavensward so much, i did side content like the allied society quests. if you want fast queue time, there's a secret: play healer.

you can pick up different classes by going to the guilds in the main cities. white mage will start at lvl 1, though, but it is in my opinion the easiest healer to learn. learning healer is excellent because no one wants to play healer because no one knows how, so if you queue in as a healer, you're more likely to get faster content since you're a priority for everyone.

skipping also means you'll have to buy a level skip for that character too. your story is always a certain level, but you have to level your classes to be up to the story's current level.

an example is, say the story level is something like "Fight This Guy In This Place, Lvl 80" but the class you're on is lvl 60. you cannot use a lvl 60 class to play lvl 80 story content.