To be honest if you're a returning ARR crafter then spamming a single crafting class to 70 is the best thing you can do. Don't bother levelling the rest via leves/gc turn-ins until you have at least one at cap so you can use them to begin farming yellow and red scrip from the weeklies. You'll be fine with your level 50 gear for the moogle daily quests and the level 60 Stormblood vendor gear is fine for the Namazu quests. Leve/GC turn-ins and the HW quests still accept vendor/market board items while you have to craft the SB items manually (I do not recommend doing this until you hit 69-70 on your first class, but save the gear you get from those quests for levelling the rest a little faster). I never used the collectible turn-ins while levelling any of my crafters, but you may want to if you want to get more yellow scrip faster. I wouldn't recommend it unless you have your retainers gathering materials and the DoL classes levelled up tbh.

It doesn't really matter which class you level first either if you're willing to sink gil into it and/or specialize in that class to speed up the process. The only thing that might give you pause is the level 54 GSM skill Maker's Mark, which is the only useful cross-class skill from Heavensward, but I'd recommend levelling GSM to 70 first anyways given how cheap the vendor items for its leves are relative to other classes.