All of the crafts are useful to have ^^.

The abilities you get as 36 ALC and 36 CRP (Hand of the Gods and Perfection, respectively) are imo the most useful across the board, for any synth, for any purpose. If you invested in those two crafts, they'd help you with the others.

You should definitely carve your own path in crafting. You can do leves and/or grind on your own mats. If you do the latter, then you should plan out which recipes you'll do (mooglebox excels at helping you do this) ahead of time, since many times you'll grind on making a material that will be useful later, or for another craft. Several different combinations of crafts have such synergies.

I maxed them before the changes to crafting, but I found that grinding BSM/ARM/CRP/ALC was significantly cheaper than grinding LTW/GSM/WVR. But the economy has changed a lot since then, so take that with a grain of salt.