Best way to level up as a dps

[Novia]

The best way in my personal experience is through doing the MSQ. Second, is doing dungeons, especially the last one that has been unlocked by levelling (or the closest one to your level). Third is doing FATEs, completing Sidequests around Eorzea.

Finally, floor set 1-10 won't be as rewarding unless you are nearly maxed out in your aetherpool. (The idea is to make quick runs of the floor set in exchange of the smaller amount of experience you receive at the end. It boils down to quantity of runs v.s. xp per run)

On the other hand, in my experience it was better to do floor set 51-60 with a pre-made party that rushes through the floor set, but of course that requires finding a party of players who have high aetherpool, and know the class they are entering with.