In what order?

[Nyalia]

I recommend all crafts to 15, then Culinarian to at least 37, then Carpenter to 50, then Weaver to 50. Steady Hand II, Byergot's Blessing, and Careful Synthesis II are all key skills for crafting HQ gear, and there are many level 15 skills that assist in this as well (Tricks of the Trade and Hasty Touch being the biggest, though Manipulation has its place as well).

If you craft mostly HQ items while you level you'll both level faster (by turning in HQ items for leves and Grand Company provisioning) and make a ton of gil (by selling HQ items on the Marketboards) to pay for materia later.

^ This.

Also, ARM is least interesting, since it has the worst level 15 skill. If you have everything at 0, and you want everything at 50, I recommend this order (steps with a/b means both "a" and "b" are good to get then, but the order doesn't matter):

• 1a. CUL to 15 for Hasty Touch (0cp quality increase results in more exp on average with level 7+ crafts)
• 1b. ALC to 15 for Tricks of the Trade (extra CP means extra touches/mends means more exp for level 7+ crafts)
• 2. WVR to 15 for Careful Synthesis I (0CP, 100% success rate, at only a cost of 10% progress compared to Basic Synthesis)
• 3. CRP to 15 for Rumination (Gets you something from those Inner Quiet stacks for your level 11+ crafts. Eventually replaced by Byregot's Blessing)
• 4a. LTW to 15 for Waste Not I (cheaper durability increaser than Master's Mend I, but has small drawbacks when comboing in Tricks of the Trade)
• 4b. GSM to 15 for Manipulation (cheaper durability increaser than Master's Mend I, but has minor drawback when used at 5/10 durability)
• 5. CUL to 37 for Steady Hand II (Amazing skill, makes Basic Touches work 100% of the time!)
• 6. BSM to 15 for Ingenuity I (Very nice for crafts getting near 50, but not that great beforehand)
• 7. CRP to 50 for Byregot's Blessing (Best quality raising skill in the game, use it as your finisher after Great Strides)
• 8. WVR to 50 for Careful Synthesis II (Amazing skill, completely replaces Careful Synthesis I and Basic Synthesis, giving 120% progress with 100% success chance)
• 9. BSM to 50 for Ingenuity II (Even better than Ingenuity I for increasing Progress, but does nothing over Ingenuity I for Quality)
• 10. ALC to 50 for Comfort Zone (For most crafts, effectively gives +14 CP. For longer crafts like three star items, it becomes +28 CP. In early endgame, it's often replaceable by just using better food)
• 11. ARM to 50 for Piece by Piece (Necessary for late endgame crafts, especially endgame furniture. Not helpful before then)

Optional

• GSM to 50 for Innovation (Honestly, you can just use Observe for the same effect most of the time. The control increase is tiny, it's mainly just used as a way of "passing" without totally wasting the CP when waiting for a better condition)
• LTW to 50 for Waste Not II (As much as I like using it, it's not actually very good. You're better off with Waste Not I and Manipulation)
• CUL to 50 for Reclaim (You'll probably never use it, but hey, it's there)

Endgame cross-class lineup for me:

1. Hasty Touch (CUL 15)
2. Tricks of the Trade (ALC 15)
3. Careful Synthesis II (WVR 50)
4. Byregot's Blessing (CRP 50)
5. Waste Not (LTW 15)
6. Manipulation (GSM 15)
7. Steady Hand II (CUL 37)
8. Ingenuity II (BSM 50)
9. Comfort Zone (ALC 50)
10. Piece by Piece (ARM 50)
11. Innovation (GSM 50)
12. Ingenuity (BSM 15) [12th skill only available for BSM/GSM/CUL/ALC]