In the original sentence, you used the indefinite article "a" to premodfy "book"- this gives the sense that there is no particular book being referred to. However, your use of the superlative adjective "best" suggests that there is only one book, so "a book" won't do. You need to be more specific- "the book" sounds better, but there will still be ambiguity until you introduce what that book actually is.
No. 1 then begs the question: whose best friend and teacher?
No. 2 also comes off as strange with the same logic as the previous two sentences: "best" implies a singular book, yet the plural "books" is used. Also, whose best friend and teacher?
No. 3 sounds the best of the four options!