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Vladimir_Nesov comments on Recommended Reading for Friendly AI Research - Less Wrong
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A suggested order might be useful. I'd at least recommend reading about algebra and topology before category theory, so that one builds up fundamental examples of category-theoretic objects.
The books are suggested in order as given.
I essentially followed this rule. "Conceptual mathematics" is elementary, "Sets for mathematics" deals mainly with set theory from category-theoretic perspective. The more general treatment of category theory is given in Awodey's book, which comes after Munkres that presents general and algebraic topology. Mac Lane's algebra comes before "Sets for mathematics" as well.