What to do when witches appear early in the game?

According to the Wiki Itself

A bow will likely be the best weapon for dealing with a witch, as the splash potions have only a short range (at most nine blocks) compared to arrows (which, when fired straight at full charge, travel 24 blocks). If a bow is not an option, a direct melee charge is the best option. Due to the witch's slow attack speed, if the player runs in a straight line and manages to get a quick sword strike in, the witch will try to heal themselves with a potion of healing, leaving the player to attack them without fear of retaliation.

So by the sound of it, if you haven't yet got a bow to fight (which early on you probably don't) the best option is to dodge their first attack, then charge in swinging your sword. With a charge, your first strike will probably be a crit that will force the witch to heal, and then you can barrage them with sword blows until they're taken down.

This might be counter-intuitive with other mobs around, since rushing in is the last thing you'll want to do against them. It would probably be a good idea to take out any wandering mobs first before dealing with the Witch, if they're all gathered together. If they're not, then it'd be best to charge the witch and take her out very quickly, before running away from the rest to attack at leisure.

The best answer is the same as with any powerful enemy (like a Creeper until you know how to fight them):

• be at full Food: that's obvious, you need Regeneration in any combat encounter.
• run back, retreat to safety: the Poison itself would never kill you, so hiding from a stray arrow will save your life.
• Bunker Push: build a "knee-crushing bunker", where you are inaccessible, and the enemy is one block above you, but cannot see you (top block in front of them is solid). This way you can hit them in the legs, while they have hard time seeing you, and thus taking aim (with a bow in case of skeletons, or lighting the fuse in case of Creepers). Thus you'll be able to slowly push to the spawner or whatever dangerous place spits these abominations.

When trapped in a "knee-crusher", Witches are as helpless as any mob (bar their ability to drink potions, just swing faster!)

(picture: a Witch in my mob slaughter zone)

As of the specific situation when you are tagged with Poison and are undergeared to deal with it - simply run! Run to safely, wait until the Poison wears off, pause, have a Twix, and follow the advice above.