For a book with furigana (readings beside kanji), the minimum is simply being able to read ひらがな and かたかな. However, the less grammar and vocabulary you know, the more you’ll have to look up (or ask about), and the more learning you’ll have to do.
I don’t have any hard recommendations for progress, but I would recommend knowing all N5 level grammar, and having started working your way through N4. You can get this by reading through Tae Kim’s Guide to Learning Japanese (free), or using a textbook such as Genki.
For vocabulary, even if you learn the 2,000 “most common” Japanese words, you may find the comic you read has barely 50% overlap with the words you know. You’ll be learning new words regardless, but the fewer words you already know, the more you’ll be looking up. I’d say having 500 to 1,000 words memorized will put you in the position of feeling you are getting something out of reading, because you’ll see a mix of words you know and words you do not know, versus a page of unknowns.
Check out the graded readers thread. I haven’t looked it over myself, but I believe it consists of texts meant for reading by lower-grade Japanese school students. (Anyone able to confirm if I’m right or wrong?) These are texts intended for beginning Japanese learners. I think I’ve seen this recommended as pre-Absolute Beginner.