Here was my experience with leveling/pacing (all done last week).
1. Azsuna - all quests and one run of Eye of Azshara at the end
2. Val'sharah - all quests and one run of Darkheart Thicket at the end
3. Stormheim - all quests, but didn't do HoV (wanted to but there was some server issue)
4. Highmountain - dinged 110 right after a certain place gets destroyed (pretty early in the zone quests).
Along the way I did two missions that rewarded player XP (very small amount), order hall quests (mage) up to the bugged one where you have to select a technology to research, maybe 10 tailoring quests, up to where the nightfallen guy asks you to retrieve his tools from Azsuna, herbalism quests for first 3 zones (1-2 each), and the exodar scenario. Minimal rested. I did about half the * rares in Azsuna and after that didn't really bother.
At 110 I did need to get Nightfallen to friendly to open up the emissary quests (other factions were already at least that high). Maybe an hour in Suramar was sufficient to do that. Also bliz says they are increasing how quickly Nightfallen rep is gained (not sure if that will affect the first bit at all).
How necessary are the bonus objectives? Should I even bother with them?
In my run I did bonus objectives I came across in first two zones, and did maybe half in last two zones. XP wise it felt like less than in WoD, but they give 200 order hall resources. They are your best source of these while leveling. I was able to keep my champions always on missions, which gave me a steady supply of extra ArP, and first two researches (third requires 110). At 110 I immediately started third tech research and artifact knowledge research. I couldn't have done all of that without doing bonus objectives.