I know this might depends on the patron spirit. I haven't decided yet. I'm still trying to figure out which fits the concept better.
Anyway, I'm planning on having a solid four picks. What are some of the the must-have arcane spells to which witches don't have access?
Well, for maximum cheese there's the shadow enchantment, shadow evocation, and shadow conjuration spells that give you access to all sorcerer/wizard spells below a certain level...but that might be a bit much. (The Shadow patron will get you a couple of these, as a note.)
If you aren't willing to go that far, haste is probably one of the big bread-and-butter spells in my group that witches don't have.
Invisibility is another one that can have a lot of uses depending on a group's play style, and the image spells are as good as your imagination (and close cooperation with the GM) make them.
I'd think a solid defensive spell like mirror image would be good, one good spell which does HP damage, then maybe look at Rennaix's other ideas.
Greater Invisibility. You can get Haste or Invisibility from your patron if you so desire, but the only thing close to Greater Invis is the 6th level spell Mislead. If you don't get them form your patron, Haste and Invisibility are good choices, of course. Maybe round it up with Wall of Force or something.
If you want it cheesy (which I presume you do, as you're taking the most overpowered racial trait in all of Pathfinder), you can get them from the cSummoner list (with Maze to round it up).
As avr said Witches are missing a lot of the defensive staples, Mirror image and Invisibility are the main ones.
Generally agree with the foregoing suggestions favouring defensive options like Mirror Image and Greater Invisibility over offensive ones, as this rounds out the weaknesses in the Witch list.
For the record, in reference to your other thread, I still think the Oracle concept was feasible, and a better fit for the healing and condition removal options your group appears to need.
As avr said Witches are missing a lot of the defensive staples, Mirror image and Invisibility are the main ones.
Depending on which Patron is picked, they do get access to those spells. I'm not saying they shouldn't take them (so they can get a Patron whose bonus spells are harder to acquire), but that if they're using Mystic Past Life for spells already acquired through a Patron, it's kind of a waste.
The best thing for them to do is to compare what Patron offers which spells they can't normally cast, select the one they want the most, and then shore up other spells they like from other Patrons with the spells gained from Mystic Past Life.
Contingency and Permanency are two I like as well as Mirror Image, Haste, Shades (Shadow Spells in general).
Note that a single dip into the Veiled Illusionist Prestige class can net you Illusion spells with little penalty if that's your thing.
The assumption of course being one wouldn't overlap ones patron with these choices... o thought that would go without saying.
I like time for a patron if you can grab mirror image through this stuff.