There's competing definitions and perceptions: there's a neo-pagan-revival religious movement who call themselves 'Witches,' there's the old-timey crone with the pointy hat and broomstick and whatnot, there's the even-older-timier sold-her-soul-to-Satan version, and, there's the goofy pop-culture witch who's a pretty young lady with hereditary psychic or reality-shifting powers.
Can you make a really good Witch using current classes (and multiclassing?)
The Warlock works perfectly for the ol' pact with the Devil and is OK for a fairytale witch.
The Sorcerer or forthcoming Mystic could work for the hereditary/psychic pop-culture witch. (The reality-altering pop-culture witch essentially casts Wish at-will, I'm guessing that's off the table.)
Druid could work for the religious version. While witches are associated with the Moon, they're not known for turning into bears, though.
But there are some features not covered:
- Crafting of potions and charms
Nod. Right now, it's easy to make a Healing potion, and that's about it. The idea of the Artificer was to help allies via infusions and enchantments that it empowered on the spot, rather than making full-on consumable or permanent items. Something like that could work.
- More & better curses and hexes
Are you thinking long-term curse that need to be removed. Might not be that defining for a PC, since there's this terrible tendency for the enemies to die very soon after meeting them...
Still, could probably make do with Wizard. However, I see two "flavor" problems:
1) All the existing Wizard sub-classes correlate to schools of magic. Will we ever see Wizard subclasses that don't fit that pattern. (If the answer is "no" it means we'll never see new subclasses.)
(unless we see new schools, I suppose) I feel like a 'Mage' sub-class, a non-specialized Wizard, is 'missing' atm. An artificer wizard sub-class didn't go over well.
2) Witches just don't strike me as the sort who learn their craft through study and research.
Maybe not research, but it's traditional for a witch to have a book of secret spells, charms and potion, like a supernatural cookbook, sometimes called a "Book of Shadows." In that one detail, they're closer to D&D wizards than most magic-using characters you see in genre. Even so, while they might have a book full of such things, they tend to be really specific and not the kinds of things adventurers tend to prepare.
Sorcerer doesn't quite fit, either, because I see Witches as having a broad range of abilities, not just a handful of spells.
Most witches you'd see in any source only have a very few adventuring-useful or combat abilities to call upon. As a whole, they could still have a broad range of abilities, individuals would just tent to have have only a few tricks they do well enough to kill monsters and take their treasure.
There's one more concept of the Witch, too. The D&D Witch, which was appeared as a dramatically overpowered "NPC Class" in early editions of The Dragon for 0D&D and 1e AD&D. IIRC, it was also used as an example of class creation in the DMG. I believe those did emphasize potions and curses, as well as dropping expanding boulders on people and conjuring up volcanoes among other things. (I'm guessing they were conceived as possible whole-party-challenging villain NPCs.) The Witch also finally appeared as a PC class - wizard sub-class - post-Essentials, Heroes of the Feywild, where it was a fey-themed, ancient arcane tradition that had some of the responsibilities and privileges of a priestly caste in the cultures that still followed it, but had nothing to do with gods are primal spirits - it also introduced the two-bit-Sith-lightning Witch Bolt spell that made it into 5e. (Witch Bolt, Healing Word, and Thunderwave appeared in the very first playtest survey, in a long, long list of D&D spells, from which we were invited to pick 'most iconic spells.' Apparently they got some votes.)
Is it possible that Witch, Shaman, and Witch-Doctor are all subclasses of a spirit-based caster class? Or am I off in the weeds with that one?
Sure, a primal or spirit-based class or classes would be possibility, the Totem Barbarian hints at that already. Amusingly, 'sorcerer' which actually implies dealing with spirits has already been used for something else, but that's D&D: class names are ultimately just game-rules jargon. Shaman would be a good, reasonably politically-correct, name for such a class. In classic D&D a shaman was just a humanoid tribal spellcaster, generally inferior to PC casters, like a 3e Adept. In 3.5, there was a Spirit Shaman that was essentially a neo-Vancian caster. There was a Shaman class in the 4e PH2, where it was a leader that had some significant action-granting abilities that involved it's spirit companion possessing an ally, as well as the usual healing and some other abilities, also involving the spirit companion, which he could conjure at a distance and use as an origin point for some invocations. I never saw it, but there was also a Shaman sub-class of Cleric in late 2e.
It's tempting to want to make Witch the base class, and "Wicked Witch" and "Good Witch" the sub-classes...
Paladins have alignment-based oaths, there's your precedent.