I'll have to check the DMG when I get home on that one. Reading through the information in the Basic Rules set, they're pretty mute on designating which ability checks apply to which tool sets.
At first glance, I think a case could be made for an INT check, but I might restrict the use based on the situation. For instance, an Intelligence (Herbalism Kit) check might be restricted to crafting remedies when the raw materials can be readily obtained from a local vendor. From that point, you're merely following a formula. Wisdom (Herbalism Kit) could be used in the wilds, as part of the challenge is knowing where to look for the raw materials, which seems similar to Survival, generally a Wisdom check.
I'll think about it and let you know.
As far as the Herbalism/Brewer's/Poisoner's kit, they are used to make different items. I don't think I'll allow cross uses. So Herbalism does medicines (potion of healng, antitoxin, etc), Brewer's does beer and alcohol, and Posioner's creates poisons.