Druids are extra awesome at Herbalism because we can do it without leaving form (as opposed to having to dismount, fight anything that aggros and remount). Alchemy and Inscription are both fueled by Herbalism.
Alchemy will allow you to make your own flasks and potions, which will be expected in more difficult content, and are quite expensive to buy on the AH. It also makes flasks last twice as long.
Inscription allows you to make War-Scrolls, which are handy in higher M+ keys where you’re looking for every advantage, but may not have a Warrior, a Mage and a Priest in the group. It also allows you to make unlocking scrolls, which are useful in Tol Dagor, and Glyphs, which are fun little optional cosmetics.
Ultimately no profession really gives you any significant gameplay advantage though, so if something else seems fun to you, do that. =)
Now that each expansion has its own profession tree, you’re probably not going to get much benefit from leveling the older expansions, especially since you likely won’t be in those zones long enough to accomplish much. Waiting until you get to BfA content to start leveling your professions seems like sound advice to me.