Translation:I read an interesting book.
Pretty much yeah. But there's also a weird implication of the other meanings nonetheless. It gets clearer with usage. Put in a historical context, the thing that causes interest in an audience during a Nō performance was called 'omoshiroki tokoro' — Classical Japanese for 'an interesting place'.
Hmm, I think the nuances たのしい and おもしろい don't map very well to English.
To me, a "fun" book is light-hearted, puts me in a good mood, or deals with an absurd topic, whereas a book full of jokes or one that makes me laugh is a "funny" book.
I'm not a native Japanese speaker, but in my experience, a "funny" book would be おもしろい本 while, a "fun" book is probably more like 雰囲気の軽い本 (fun'iki no karui hon "a book that has a light/non-serious mood"). In Japanese, a book isn't described as たのしい本, but rather 読むのがたのしい本 ("a book which is fun to read").