Candide is a philosophical work whose plot moves very quickly. It moves so quickly, in fact, that skipping single chapters means you skip Candide's entire military career, an entire character's arc, or Candide's entire trip to a country. It is difficult to recommend specific chapters to read in order to get the ideas behind the work. Skipping chapters will likely leave you quite confused unless you have read the work in its entirety before. However, what I would recommend is to get a sense of all of the different characters, who all more or less represent different philosophies of Voltaire's time.
Chapter 1 is likely essential so that you can get a good sense of both the main character, a naive Candide, and his tutor and mentor, Pangloss. Pangloss represents a mouthpiece for Leibnizian optimism (the central idea that Voltaire was attacking in his work). At the beginning of the novel, Candide buys into all of these ideals hook, line, and sinker.
Chapter 2 shows Candide's first experiences outside of the protective castle of chapter 1, and Candide experiences the violence of war while still believing that he is in "the best of all possible worlds."
Chapter 3 introduces Jacques the Anabaptist, who approaches others with kindness and charity.
Chapter 4 shows what happens to Pangloss once he himself is met with misfortune.
Chapter 8 shows the reunion between Candide and Cunegonde, who has suffered greatly since Candide left the castle and has now been sold to two men. A former pupil of Pangloss, she starts to doubt his teachings.
Chapter 14 is where we meet Candide's valet, Cacambo, who is a steady present throughout the work and approaches things in a much more rational way than most of the other characters in the novel.
Chapter 17-19 shows El Dorado, which seems at first to be a perfect, ideal world (just the kind Candide has been looking for). However, they decide to leave with jewel-laden sheep in order to be rich in the worlds they have just come from. Chapter 19 shows what happens to that plan.
Chapter 20 introduces us to Martin, who, unlike Pangloss, maintains that God has abandoned the world. However, even though unwavering optimism appears to be foolish, there are definite drawbacks to Martin's pessimism.
Chapter 24 brings back Paquette (whom you should remember from chapter 1) and introduces us to Brother Giroflee.
Chapter 26-30 is a whirlwind of activity that I recommend reading in its entirety so that you can know everyone's resolution. The last chapter, chapter 30, is particularly important, as it ends on Candide's "final" philosophical point of view (though whether he sticks with it or not after the novel's conclusion is anyone's guess).