After playing so many strange combinations of traits, challenges, dynasties, and just goofing around my sims no longer have any 'must learn' skills or skill challenges.
Back in the day the cooking skill and the handiness challenges were great helps and at least one sim in each household would learn them! (Now I can just plonk down a mini-fridge or a bagel bar and let them fend for themselves
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I'd say the alchemy challenge rewards when playing an elixir maker are pretty essential. If my sims plan on brewing a lot of elixirs with rare ingredients I'll generally have them make 150 potions of bliss with produce from the store to raise their skill and get one challenge out of the way. Then they'll read alchemy skill books in the library until alchemy is maxed, at which point they'll finally start researching alchemy and read the seven elixir recipes to learn all the recipes and complete the second challenge. With those two skill challenges done they'll be brewing up triple batches of elixirs with a good chance no ingredients will be used up, which is fantastic for those recipes with the really tricky to find metals and insects.
Those charisma challenges are great, definitely. Few of my sims really need them, but I do find them a huge help when it comes to playing the World Adventure quests. There's so many 'become friends with X in order to Y' requirements; being able to jump to friends with a single charming introduction is such a time saver!
Oh, and while it isn't a skill, if any of my sims plan on smelting or cutting gems I'll make sure they get the gem and metal collector challenges done before they so much as split a geode.