I've been pondering upon Quickleaf's (always) insightful queries and how/why I would be generating a Witch class fo rmy own homebrew game...which I have off and on tinkered around with for years.
A "witch" class was always something that would be supplemental, one of those [1e] "Unearthed Arcana" type classes, if you will, but Ive recently been toying and debating [with myself] and seriously considering making it a fundamental "original" class within my homebrew game system.
To that end, of course, the pivotal basic question of "What is a Witch?" gets thrown around quite a lot...along with its companion ponderings, "What is a Witch NOT?" and "What makes it different from any other Mage/Wizard/Sorcerer type?"
I think...and naturally, this is me, so what I think now/today can be different ten minutes from now...BUT I digress...I am fairly confident that my favorite simplest interpretation and the "defining" statement that allows for a range of Witch archetypes, from myth and folklore, to Shakespeare and Disney, to Oz and Narnia, is the following:
1. Mages[Wizards] study/learn to use magic to acquire and increase their power.
2. Witches study/learn to MAKE magic to acquire and increase power of and over themselves and others.
The pivotal concept and term that is often -notably- missing from discussions of fantasy RPG witches is...the very fundamental (and perhaps troubling to some spineless publishers) term...WITCHCRAFT!
Or rather, witchCRAFT. Witches MAKE magic. They CRAFT their magic to their ends. Through brews or candies and cakes, poppets and switches and brooms, weaving shawls and blankets, crafting spells (protective and dangerous) into candles, carving or writing out talismans in clay tablets or metal medallions...or apples and gourds, combining and processing the herbs and hairs/furs, bone and blood of the natural world...witches take what they've got and CRAFT magic into and/or out of it.
I really like, and have included in various iterations myself, precisely what Elfcrusher suggests. Witches gain cantrips. They are, after all, the "common person's" magic-maker. Their magic is, before anything else, USEFUL...that doesn't mean it has to be "good" or all witches are harmless wise-woman type healers and moon-priestesses. What is "useful" for a witch can have entirely selfish motivations or diabolic ends.
So, like Elfcrusher, my witches all started out with access to Cantrips only. For 5e, I would make this cantrips of any spell list -but still counting as arcane/int-based magic when used by the witch. Ritual use is also a no-brainer, and same applies. If it has the ritual tag, a witch with an herbalist pouch and cauldron (part of their starting equipment) or with their magic focus/item/device (explained later) can perform it regardless of the spell list on which it appears.
Following that, a slow spell progression that allows spell choices in my own homebrew from Nature and Illusion Magic lists. For 5e, as each class has its own particular spell list, I might even make them a half-caster progression, 5th level spell max (til 14th level). I would probably adapt a limited list including elements from the Sorcerer (or Warlock if you prefer their flavor), Bard, and/or Druid lists...focusing on enchantments, illusions, and transmutations and limiting the amount of big flashy evocation type stuff.
Maybe subclasses could incorporate a more conjuration and/or a necromancy-heavy witch. Sub-classes would be called "Crafts" or [already used] "Traditions" or, if you really like the flavor, "Covens."
Class features would include
1st level: Witch's Craft: a spellcasting focus, which would need some kind of cool Witch-crafty name and we couldn't call it a "totem" cuz, ya know, barbarians and shamans and stuff use those. Some common worn or household item: a shawl or hat, piece of jewelry, a knife or broom or cup, staff or switch/stick/simple wand, that the witch always has with them and grants them bonuses to their spellcasting and AC. They are very protective/defensive of it and considerably reduced in power without it. It functions much like a cleric's holy symbol in that without this item they are restricted to using cantrips and rituals only (no leveled spells, but counting Brews as ritual).
1st: Hexing -which may be a boon or a bane, depending on the witch's desire, to others' d20 rolls (saves, attacks, skill checks, etc...). Be it a gaze or hand gesture, cackling, spitting in the target's general direction, or whatever, each witch has their own method of hexing and she must be able to conduct it in order to hex anyone/anything...so a vicious gaze/line of sight (giving the "Evil Eye") is a common choice.
2nd or 3rd: Witches' Brews: the ability to recreate a spell effect not on the Witch's spell list by combining ingredients/cooking them into a mixture: be it a potion or some kind of gruel, porridge or stew, baked into cookies or cakes, what have you. The witch gains additional brews of their choice, for spells in which they have slots, as they gain level: 6th, 10th, 14th. Make one brew per long rest and each single brew may include as many doses as the witch's proficiency bonus + Int. modifier.
6th or 8th: Was going to do the Eldritch Knight magic weapon summoning thing here, but think better... something more flavorful (that I like much better, actually) let's call it, "Incantatum Arcanis": the witch can attempt to enact a spell they do not know (but for which they have an available slot) by coming up with a rhyming incantation describing the desired effect. They can do this [...however many times would seem reasonable?] before requiring a short rest. The roll to beat is...something...maybe DC10+spell level and the witch may add their spell attack bonus to the roll. Failure is up to how you'd want it to play. I would probably go with "nothing happens"...so you just look like a crazy person reciting some vehement rhyme. (Why doesn't anything happen when normal people just make up rhymes? Well, they aren't witches, are they now?) But you could take a roll on the Wild Surge table to make things interesting...or develop some backlash [reverse?] effect. It's never a sure thing, but a powerful/experienced witch should be able to pull off most small types (1st-3rd level spells) of magic without too much concern.
14th: Mystic Arcanum for 6th (16th for 7th, 18th for 8th, 20th for 9th) level spells as per the warlock. Once selected ,the witch can use these upper tiered spells, each, once per long rest.
Or, here, something like the Eldritch Knight's magic weapon summoning with their casting focus. Also the ability to recreate a focus with minimal effort/minor ritual in the advent of a lost or destroyed item...making a new length of wood into a broom, turning a tattered cloak into a spell-focusing cowl, transforming a handful of silver into a sparkling necklace, etc...
20th: Witch's Capstone?...something pretty awesome...maybe the ability to form brews or items to create any spell? Any spell they know? Or just let the access to 9th level spells -that's pretty damned powerful stuff- be their capstone.
Something like that. Add in the PC having a familiar, if you want, for flavor...it's a ritual on the spell list readily available...or, most simply, if you want them to have a more fundamental-material consequence, include normal household/garden animals in among the "common household items" that might be used as the witch's spell-casting focus.
But, as you see, the focus is not on accumulating huge amounts of spells to form tomes to supply one's power (though a spellbook would be a requisite cited under the Spellcasting feature of the class) but making, one might say "crafting," one's own magic.