When a new expansion hits, there are three factors which can influence whether you fall behind or not. First, the time you put in. The more you play, the faster you get things done when compared to the casual player, who logs in every day, kills some monsters for a couple of hours and logs off. What would take a month for a player like this, you could get done in days, if you play a lot. Second, you have to know what opens when. Only then you can NOT miss anything important that you’re supposed to be doing. If it also requires preparation, you can make sure to be ready. Finally, you have to plan out what you need to do and figure out the most effective path to accomplish it.
The first thing is up to you, however, I can help you with the other two. On August 23, Blizzard released their Dungeon and Raid schedule. Following the release of the game on 00:00 of August 30, Legion dungeons will be available on Normal and Heroic difficulties, while Mythic Dungeons will unlock after the weekly dungeon reset comes. The next content to become unlocked will be The Emerald Nightmare raid on Normal and Heroic difficulties. Together with that, Mythic+ dungeons will also become available. September 27 is the day when Mythic Emerald Nightmare is unlocked, together with the first wing of the Raid Finder version of the instance. On October 11, the second wing will open on Raid Finder, followed by the last one on October 25.
Okay, you are level 110. Time to put in all of your Artifact Power into your main spec artifact. Then, go and start your artifact research. Following that, start completing your Class Order Hall quests and level the whole Hall itself. When you can’t move forwards with that, move to Suramar and do as much of its content as you can. Once you are friendly with all Factions, start the prequest for World Quests and any dailies which award chests. Once all of that is done, you can go and level your alt. At least that is what Medivh suggests. The detailed spreadsheet can be found here: https://docs.google.com/spreadsheets/u/1/d/1TiiI4huz4NXKfx7PGvvVTyP6xu8VaDNZ4-FEn69mOhc/pubhtml#.
The important thing is to never fall behind Artifact Research, keep up with World Quests, offering any decent rewards, farm heroic dungeons for AP and gear, do Suramar to unlock the two Mythic only Dungeons, and keep up with Class Hall and profession quests. There is a LOT to do in Legion. Players will probably reach a point when most of the content is outgeared, however, it will take a fair bit of time. If Blizzard learned anything from WoD, they will have some kind of new content to keep players from going away just as that starts happening.