I am still trying to figure out how to get all my garrison and navel buildings and followers to max, and I am interested in checking out as much of the content I can before legion.
After getting 10 garrisons and shipyards up and running since February I think I've got down the best way to approach maxing them out the fastest. But my method requires flying because it involves farming Radiating Apexis Shards in Tanaan Jungle.
The buildings I recommend are Barracks lvl1 (because you get it for free), Stables lvl1 (Because you can interact with objects and farm while mounted), Salvage Yard lvl3 (For follower gear and also a chance at TMog gear which sells very well), Jewelcrafting hut lvl2 (For 200g per day with Olin Umberhide assigned), Frostwolf Tavern lvl2 (So you can immediately start hiring treasure find/scavenger followers) and Trading Post lvl3 (So you can get some passive Garrison Resources but more importantly get 20% to all rep gains which makes getting your oil rig a few days faster). I skip the lumber yard completely because while it is passive GR gain you have to farm the lumber for it and if I'm gonna farm I'd rather farm GR itself.
With stables so you don't dismount while gathering you can get 5-6k Garrison Resources per hour farming Radiating Apexis shards using this route:
It takes a few laps to understand exactly where they spawn but after you know where they spawn you can zip around the entire route in about 2 minutes. Added bonus is that these also drop baleful gear. I recommend using the Routes addon and making your own custom route based on the TomTom coords in that video. This way you don't have to keep putting the waypoints back in every lap.
With those resources I recommend first getting an optimal shipyard setup for gold returns:
Best shipyard setup for 100% all gold missions? : wow
I wouldn't try getting the right ship crews until after you've got a level 3 shipyard because it's better to be able to just throw whatever ships you have at any and all treasure missions without caring if they fail and sink to go from level 2 to 3. It makes it go a bit faster. Spend your garrison resources on Shipyard Rush Orders until you've got most of the right ship crews then start outfitting them with the correct ship enhancements.
After that's done start using the Garrison Resources to reroll your followers traits. You can buy trait reroll scrolls from your garrison quartermaster for 1k GR each. After you've got a couple treasure hunters/scavengers I'd replace the stables with a War Mill to start using that to get gear upgrades for your followers.
Also, if you have gold to spare look for
Frozen Arms of a Heroon the AH. I typically buy them at 450 to 600g. They increase both armor and weapon ilvl for your followers by 50 and are completely worth spending the gold on since you need ilvl 675 on 3 followers and 650 on another 7 to get the best missions to show up. Also upgrade your Tavern to level 3 once you have a few ilvl 650+ followers to get the best treasure find missions.