(My answer have some limitations, because I myself can't answer beyond that, but without going there if you read my answer you will probably get the answer of your question, not too deep though.)
Do you have [Noun Phrase (NP)]?
Now this NP here is -
Here the PP (prepositional phrase) is the complement of the head noun (suggestion). A PP often acts as a complement or postmodifier of a noun phrase.
The prepositional phrase structure is like this -
There has to be a head preposition - as to/about. Without it the phrase structure is incorrect. And the complement to the head preposition is an embedded wh question.
So from it, it's clear that you can't omit as to or about from the sentence, or it will make it ungrammatical.
Without the preposition there is no connection between the head noun and which book I should buy part. A preposition connects them together.
(My answer doesn't address why the complement to the head noun in the NP tree has to be a Prepositional Phrase. The simple answer is I don't know. I couldn't find the reason beyond what I said here in any grammar book I checked, though I haven't checked many books. I think this will be dealt with not in grammar books, but in good linguistic books, and I don't have any. Nor do I have any knowledge in linguistic theory. Someone else might answer it better.)
Best Answer
You can use either one; neither is incorrect.
You might also use a contraction:
Some people recommend avoiding contractions in formal writing; however, unless you are writing, say, a contract or an academic paper, that rule would not apply.
Also, some might consider the 'that' to be a fluff word, so they would recommend leaving it out. The Grammar Girl wrote a column explaining how you should leave it in when using "non-bridge verbs," which, according to her, "carry extra meaning beyond simply the idea of saying or thinking something, and [therefore] don’t sound as good when you omit the word 'that'."
Lastly, the structure you are using could be completely omitted in some contexts. While it's not grammatically incorrect, it's wordy, and sometimes writing can be improved if you simply say something more directly. For example:
This could be shortened to:
Or even:
So perhaps the bigger question isn't whether or not to include the word 'that' – it's whether you should include the phrase at all.