I would do the quest if you want the story, looking back on it now I think some crafting abilities will be rewarded as quest rewards after 1.20. Buffalo leather is an old recipe that will be eventually removed, and old recipes still use the training manuals. Unfortunately, the crafting quests and guildleves still use old recipes but they are going to be revamped in the next patch, which should hopefully be released in 1-2 weeks. In the meantime, I would go ahead and pick up at least any immediately needed training books you need for quests or guildleves because you get a TON of guild marks now if you do leves in the city that houses the guild. So for leatherworker, doing leves in Gridania would reward you with marks.

Lodestone's Synthesis section is a good way to check if a recipe is "Current" or not, as it only has new recipes. If a search there turns up in failure, that recipe is old.

Also, if you are curious, here is a huge list of items that are getting phased out. This streamlines the crafting AND gathering process significantly. If you have any of them, I suggest getting rid of them in whatever method is best for you.