I think the Q&A @user3856370 has pointed you to should sufficiently answer your question. I'd like to say a few words about how I personally understand that sentence. Here goes nothing:
Very often you see Japanese verbs used unaccompanied by a subject or an object, or both. See this answer for a more detailed explanation on this.
Your proposed version dispenses with the あったら conditional and has the patient of the verb どんな本 as the subject of the sentence. It is thus a single-clause sentence with どんな本 as its subject. Let's look at the original sentence:
You are right that あったら often marks a clause. In the original sentence, although there is no 読点 (comma), 「どんな本があったら」is 主節の述語を修飾する副詞節 (an adverbial clause that modifies the predicate of the main clause), because it describes a condition that, when met, leads to the next step (thinking about buying them).
If we put back in the sentence things that are omitted:
What kinds of books, if the store has them, would you like to buy?
Since either が and を can be used here, it doesn't really matter if you regard the pronoun それ, a placeholder for どんな本, as a syntactic subject or object. Semantically of course, it is the object/patient of the verb 買う.