The audience is atheists, agnostics, and those on the fence between faith and doubt.
Ah, then you need an approach which is grounded in philosophy. A approach which relies on the Bible or the Early Church Fathers would not work.
Since they don’t have any firm belief in God, that’s the first thing you need to take care of. This is why apologetics for atheists is more difficult than any other - the starting line is way farther back. Once you can establish belief in God, then you can start to talk about how we relate to God (which would be the Church).
I recommend
“Christian Apologetics” by Norman L. Geisler. Dr. Geisler is an evangelical protestant, but he is a renowned philosopher. Since you (at this point) require only a philosophical approach, this is fine. There’s nothing in this book that a Catholic would object to.
But this book is not written for a “popular” audience. It is a book of logic and proofs, one after another. I would say it is entry-level college material. It takes a disciplined mind to read this book. An atheist who read this book would do so only because he wants to prove Geisler wrong with his own logic and proofs (atheists tend to be an arrogant bunch, so this type of thing would appeal to many of them). So, in a way, the book is a trap. Offer the atheist a puzzle to solve (find the flaw in Geisler’s logic). But Geisler’s logic is absolutely sound. In the end, the atheist will be forced to either give up, or believe in God. (if he gives up, he will justify it by saying that Geisler is a professional philosopher, and thus able to construe flawed proofs that are difficult for a layman, such as himself, to unravel).
If the person does not have the determination (or, daresay I, the intelligence) to follow Geisler’s book, then you need something else. Unfortunately, I have no alternative to offer (but maybe folks here do).