This is why he prefers them:
Salvage Yard - Pretty much mandatory. You get items for completing garrison missions. The items are great, but mostly important because they give you a LOT of follower upgrade items. Your followers start at ilvl 600 and you need to up all of them (20 or 25 depending on your buildings) to lvl 675. It's gonna take a while even with a salvage yard but a salvage yard makes it bearable.
Inn - Lets you recruit followers once a week. You also get a daily dungeon quest which is also nice. When you recruit followers, you can recruit followers that ONLY have certain things you're looking for. Need a follower to counter an ability? Inn's your spot. We end up mostly using the inn for recruiting followers that have rare abilities such as "Epic mount" (Halves mission completion time and stacks) or the resource gain abilities (Like how Mastric was able to get 4000g from one mission)
Barracks - A double threat! Firstly, it ups the number of followers you can have active at once from 20 to 25. This alone is great. It also lets you use one of your followers with the "Bodyguard" ability to tag along with you and be a companion while you quest or whatever. There are several different bodyguards you can use. Playing a tank class? Pick a DPS bodyguard and they do surprisingly good damage. Playing a ranged dps? Pick a tank bodyguard to keep things away from you! Etc.
Storehouse - There's not too many good Small building options so this one is just convenient. This let you have a bank, guild bank, transmog and void storage access all in your base.
Trading Post - Lets you trade one resource for another which helps for gathering professions but more importantly, it lets you trade in resources for garrison resources (Via work orders). This is a GREAT way to get Garrison resources quickly.
One that bash didn't mention but should be on the list:
War Mill - Lets you trade in iron horde war scraps for follower upgrade items as a daily quest (Which you'll need) as well as use garrison resources for creating follower upgrade items. Check out this guide: http://www.icy-veins.com/wow/garrison-complete-guide