What desynthesis classes are the best to level and how high should I take them? I wish you could max out each one.
Depends on what you want. They haven't made any new desynthesis exclusive items since the end of ARR so you don't really need to max any of them to make new items or even bother with the whole system honestly.
The few exclusive items from it that I recall still being relevant are Mastercraft Demimateria which comes from desynthing ARR DoH/DoL endgame gear (GSM is good for this iirc), Battlecraft 3s which come from dungeon or raid gear (GSM cause of primal accessories, BSM cause of primal weapons, and to a much lesser extent WVR, LTW, and ARM), and Fieldcraft 3s which come from DoH/DoL gear and Wedding attire (LTW is best for this cause iirc wedding sandals are the cheapest item that can drop them, WVR can de synth pants for them but they cost more than the sandals, and I think GSM can get them from glasses).
CUL desynth is okay if you fish a lot cause you can turn junk fish into crafting crystals.
Don't remember ALC and CRP having any useful desynth drops fwiw.
As for what lv you should take them, figure out which items you want to desynth and just reach a lv that gives you 80% + success at desynth.