[Nathan]

I ran up and grabbed my みんなの日本語 set (1 and 2) just to check what you were referring to. By second book, I assume you mean an additional teacher-guide style book, because both of these are exercise books, pure and simple.

They didn't have anything other than the exercise books at the shop in Osaka where I picked them up.

I can agree on the no-romaji or English to fall back on being a bonus, but not for a complete beginner with no assistance. You need to have at least some basic knowledge (hiragana, katakana) and a dictionary. Without, it would be like throwing you a child's book in arabic script and saying "Okay, start reading!"