No mandatory cross class skills:
1. Byregot's Blessing
2. Comfort Zone
3. Ingenuity II
4. Careful Synthensis II
5. Steady Hand II
6. Tricks of the Trade
7. Hasty Touch

The debate starts here for the last 3 skills
Rapid Synthensis - 80% success (under SHII), for 250% completion; can significantly reduce number of completion touches required at the cost of RNG.
Piece by Piece - two touches grants 55% completion, after that, the diminishing returns is so bad, Careful Synthesis II is always better.
Reclaim - 90% chance to save your mats from poor RNG.
Waste Not - Better for 35/40 dur recipies
Waste Not II - Better for 70/80 dur recipies
Flawless Synthesis + (can't remember the name of the skill which allows like 10 FS without reducing durability) - the problem here is the cost two cross class slots to use this.
Rumination - Allows you save yourself from Poor condition on Byregot's Blessing, if you are using Reclaim, otherwise, your rotation needs works.
Manipulation - IMO, no very useful, Master's Mend only cost 4 CP more for basically the same effect.
Bands - waste of a slot unless you are going to be doing a lot of crafting for a specific elemental affinity item.

I personally use:
8. Rapid Synthesis
9. Waste Not
10. Reclaim