On PoliticsChomsky's Government in the Future is probably his best essay outlining his political philosophy. It's worth reading this essay but also worth reading some of the works referenced within it, which can be found here. In addition to this I'd recommend Kropotkin's Mutual Aid and his Conquest of Bread, which Chomsky mentions on occassion. To look further into Noam's political views there's also his book On Anarchism, and you can also check his references from other books using this sites categories feature, for example: Anarchism.
On InfluencesAccording to Chomsky, John Dewey and Bertrand Russell "were two of the major, if not the two major thinkers, of the twentieth century." Their works, therefore, deserve some attention. For Bertrand Russell I'd recommend Roads to Freedom: Socialism, Anarchism & Syndicalism; In Praise of Idleness; Power; The Problems of Philosophy; The Analysis of Matter; and The History of Western Philosophy. For Dewey, Democracy and Education; Knowing and the Known; The Public and its Problems; and The School and Society.
On LiteratureGrowing up in a family, of largely ordinary working people, Chomsky describes an intellectually exciting and lively environment defined by high culture: "Freud, Marx, Tolstoy, Faulkner, the Budapest string quartet, the latest Shakespeare performance, etc." He has, he states, "been powerfully influenced by fiction, including what I used to really immerse myself in when I had more time -- Tolstoy and Dostoevsky, Turgenev, Eliot, Dickens, etc." He often mentions in particular Dostoevsky's Brothers Karamazov, the Grande Inquisitor section. In a recent interview Noam also said that he prefered Yevgeny Zamyatin's We over Orwell's 1984 and Huxley's Brave New World. For more recommendations see the Literature category.
On ChomskyIf asked to give a short list of my favourite works, I'd say the following, in order: American Power and the New Mandarins, Government in the Future, Year 501, Pirates and Emperors, and Hegemony or Survival.
On FilmNoam's favorite film is The Salt of the Earth. Or to see Chomsky on film check out Manufacturing Consent or The Corporation.