the right time to become an alchemist?

1st, carpentry only increases bleed dmg. Prod doesn't affect cursed rain dmg at all.

2nd, hw and bish are proably the best classes to level prod with due to their limitless Aoe. Sniper would also be pretty good. Alchemist has decent Aoe range with meteor and cursed rain, but they are slower and cost 5k per spell. As an alchemist cursed rain is probably your best farming skill due to the 30 sec duration. Then use drain or kill sticks to aggro new mobs.

3rd, once you get alchemy Smithing and carp to 100 that proably a good time to switch, but it's completely up to you. I swapped before leveling any prod and have them all capped except for chasing. Ultimately prod adds up to about half of your poison, burn, and bleed dmg. Blizzard and cursed rain will deal full dmg as long as you build with int and dex. So prod levels are nice boost to your dot dmg but not everything.

Finally, it takes a long time to cap everything. about 1 to 2 months per prod is what it took me as a alchemist starting at 0. The 1st 100 levels go quick but it slows down alot as you need harder to farm mats to make the next item.

Alchemy was the fastest for me once you get carpentry high enough to make paper, but the others all hit slow points after 100 becuase you will need rare boss drops to continue.

Which is why I recommend switching after 100 becuase alchemist are awesome boss farmers! Since alchemsit dot dmg doesn't depend on gear you can wear a resist set and still deal high dmg.

Good luck farming!