So I only saw one other guy give you apologetics material, and another person made the point that life is pointless if there is no God (which I agree is true).
But you're asking for intellectual material.
I would start with Dr. Edward Feser's Aquinas (A Beginner's Guide). It's $12 paperback on Amazon, $5 on kindle if you have a kindle-enabled device.
After this, if you find yourself convinced, I would go with The Last Superstition by the same man, for $15 paperback on Amazon or $12 on kindle.
Next, you can read excepts from the Summa Theologiae at your leisure for free on http://www.newadvent.org/summa/.
If you're very intellectual, Ed Feser's book Scholastic Metaphysics can really get you into Thomism after you've done the above, or you can pick up some MacIntyre.
Well, a first point is that as Catholics we believe we can know God's existence through reason:
>>The same Holy Mother Church holds and teaches that God, the beginning and end of all things, can be known with certitude by the natural light of human reason from created things; "for the invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made" [ Rom 1:20]; nevertheless, it has pleased His wisdom and goodness to reveal Himself and the eternal decrees of His will to the human race in another and supernatural way, as the Apostle says: "God, who at sundry times and in divers manners, spoke in times past to the fathers by the prophets, last of all, in these days hath spoken to us by His Son" [Heb 1:1 f].
(From Vatican I)
As such, nobody has any excuse for not believing, and they're ultimately accountable to God for it:
>>18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who [d]suppress the truth in unrighteousness, 19 because what may be known of God is [e]manifest [f]in them, for God has shown it to them. 20 For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and [g]Godhead, so that they are without excuse, 21 because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened. 22 Professing to be wise, they became fools, 23 and changed the glory of the incorruptible God into an image made like [h]corruptible man—and birds and four-footed animals and creeping things.
(Romans 1:18-23 NKJV)
But you're right, people don't have the time to read through the arguments, and either way, we shouldn't believe on the basis of arguments. Paul said this about his preaching for example: "And my speech and my preaching were not with persuasive words of [b]human wisdom, but in demonstration of the Spirit and of power, 5 that your faith should not be in the wisdom of men but in the power of God." (1 Corinthians 2:4-5). Our faith is compatible with reason and supplemented by reason, but it's ultimately known supernaturally, as Vatican I says.
So if someone asks us about our belief in God, unless we have the time to look through the arguments, we'll need another method. (btw, for good philosophical arguments for God, Edward Feser is really good - https://www.amazon.com/Aquinas-Beginners-Guide-Guides/dp/1851686908 you can get this really short book pretty cheap) Part of it is recognizing that atheism has no legs to stand on. If God doesn't exist, what can we base anything on? Where would we get morality, logic, etc. ? They'd be evolutionary developments and preferences, not absolute truth.
But then you could simply say - you know about God because of supernatural revelation, the Holy Spirit testifies, etc. you don't need arguments. As St. Paul said again: "For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God." (1 Corinthians 1:18) If you think about it, a lot of what an atheist believes is also known without argument. My atheist relatives have never seen the earth go around the sun, or that the earth is round, but they believe it. Why? Some people who they trust said it. That's how we get most of our knowledge really, and that's not a bad thing. We trust the testimony of the Apostles in Scripture and Tradition that God is real. Hope that helps.
Got some time? Read this excellent blog post series.
Or read Aquinas by Ed Feser.
Why not both?
Aquinas heavily covers all that stuff, and Feser's book Aquinas is a great start, followed by the Summa of the Summa and then the Summa itself. After all, the author Aquinas quotes the most is ... God Himself in the Scriptures!
This book is a good start: https://toptalkedbooks.com/amzn/1851686908
His books are also really good - they're high-level, but something like Aquinas will give you a good introduction.
I recommend reading Augustine's *Confessions * and *Answering Atheism * and *Aquinas *.
I think you'll really enjoy them.
You recognize that the Catholic school's educational program is better; and there are reasons why. It's because Catholics believe that the world is created by God, and knowable; and that each one of God's people deserve our love and charity because we love God, Who is Love Itself.
Be prepared to grow with your children; life is a journey. Spend some time at Adoration; just sit and think. As Catholics we believe that the infinitely powerful Lover of Mankind is searching for each one of us, all we have to do is sit and let Him find us where we are, and lead us to where we want to be.