In terms of effiency it's best to level a dps via MSQ quests while doing the dungeons on either tank or healer as you have lower queue times on them.
Youc an easily level 2 classes without regularly doing extras like roulettes or WT but if you do some extras a bit more regularly (doesn't have to be daily though), you will hit 90 with 3 classes by the end of EW. You also have the benefit of instantly having 2-3 classes (and roles) to choose from for content, depending on what is in highest demand for the content you're doing.
Alli raid has fairly short queue times for DPS, other roulettes favour tanks and especially healer. Any specific duties I recommend healer for better queue times same for playing at odd hours.

So the "just level one class" is nice for people that want to include a bit of RP as it feels more like a consistent concept but if that's no concern for you than I would recommend leveling at least 2 classes. Since you can also pick up some classes at 30/50/60/70, it's fairly easy to get 3 to 90 during MSQ.
I leveled only DRG during MSQ on one character and I can't recommend that if you want to play more efficiently. Duties were always a roadblock outside prime times, I was way overleveled and it just felt wrong and unsatisfying to be close to 60 while not even having my HW skills unlocked as I hadn't reached the area for it yet. Quest rewards were wasted as I already outleveled the armor by a mile.