Funny you should post that, I was just talking about that exact rotation to friend, and how it's a good example of theorycrafting vs reality.
That rotation is, on paper, the most optional damage output if you hit all the cooldowns perfectly and don't die while going through the rotation.
Whereas in-game, due to changing battle conditions, things that need to be dodged, or blocked, or reflected, or pulled, and so fourth, I find it very unlikely anyone will ever manage to do that full rotation even once, unhindered. I actually tried it for a while for the lols, and it was so unnatural, I think I became the worst Engineer in the game for a while. While conceptually I get why someone would want to do an optimal rotation like that, it really is pure theory in my book.
Unless the tank does his job, of course, leaving the DPS to play with their tinkertoy macros.*
*Sarcasm.
All dungeons are 100% optional, and act as a side-story. I'd recommend doing them when you hit the levels for them, if just because they're actually pretty cool, and I'm sure you can find GAF people to tag along and explain things. They're not overly complex though.
As for the story (called Personal Story), it has 'chapters' that unlock at specific levels (every 10 levels) - you'll be told where to go and who to see when the time is right. I recommend playing the start( it's a little instanced zone), then following the in-game guide arrow and exploring the starter zone. You can go to any race's starter zones, so if you feel overlevelled for one zone but underlevelled for another, explore the other starter zones.
I find the Personal Story pretty good, but it changes depending on what race you pick, and what choices you pick while making your character. They all end up in the same place eventually, with some branches based on choices. Some paths are more interesting than others, based on personal tastes.
You'll see these gold Renown Hearts on the map. Just to note, they are aren't 'quests', just areas where stuff happens and when you complete some objectives, a vendor unlocks under the heart. Dynamic Events (think FATES) happen all around the world, hooking up with one is a great way to level, and they're often part of a chain. There are no quest NPCs with ! over their heads, basically, there /are/ no quests. Just stuff to do.
So when you find a heart, check the top right of the UI and see what it wants. Dynamic Events often start at hearts or move past them, tag along with one if you spot them (you'll see a notification that there is one near, or happening).
Gotta warn you though. GW2 and FFXIV are almost polar opposites in a lot of ways, so try to approach GW2 with a "Beginner's Mind", and don't expect it to behave like FFXIV.