Well, I think one of the reasons the argument usually goes into the realm of science first, is precisely because THE place to look for evidences or arguments are in the reality around us. By reason we understand instinctively that if what we're saying about the Catholic Faith IS true, then automatically, ALL of reality will reflect this truth, to whatever degree, accordingly.
If you say, show me the philosophical arguments or arguments of reason... well... how do you argue for the existence of something or the truth of something, while trying to keep that material reality out of the picture? It is almost impossible for me to think of an argument that does not to some degree concern the implications or proofs in the concrete reality around us.
Even if I say that, for instance, the fact for instance of many of the "life after death" stories that cannot be explained away, where persons who had been declared medically dead, were able to report who came in and out of the room their body was in, or what siblings or friends were doing and where they were at the time they were supposedly "dead". This represents an impossibility if we are going to insist that the "soul" is only electrical impulses in the human brain. Even if a person were not really dead, whether they were alive or not, there is NO way they should have knowledge of what was going on in other parts of the building or in other buildings. This is mysterious, but it suggests that clearly there is more to the human being than purely physical aspects. There is something that can and does continue to exist after death.
This is only one example. But the arguments come again and again for proof, to the concrete reality around us as we know it (and of which God, BEING real, is also a part, whether we can see Him or not). So I'm not sure where or how one would begin to try to argue outside of the evidences or reasons our minds naturally go to, which would be those things we can experience and know through our senses.
The closest I can come to pure philosophy, are questions like... what is the difference between something living and something dead? What is that indescribable "something" that constitutes the "life force" of living things? What implications does this have about what else might be part of the reality around us, but which we cannot see or experience directly through our senses?
Still, even questions of "why are we here" and the like... all seem inevitably to go back to looking for proof or evidence in the physical world as we know it. This is why I jumped directly into the scientific arguments.
Especially in biology, the scientists are being faced increasingly with the gaping holes in their atheistic/darwinistic theories. If you research the subject through the other (creationist/intelligent design) side, what you come to realize quickly is that the key or core theories that the atheistic or darwinian scientists have long rested their beliefs upon, are not holding up under scrutiny, whether it be scrutiny of the fossil record, which increasingly shows the truth and reality of Noah's flood, or whether it is arguments in biology, upon which rest the whole theory of evolution at it's heart... the idea that organisms CAN evolve... is falling apart. And these realities are not being told to the general public. They are being denied by the mainstream media and academic world, and by "mainstream science." The truth, which does NOT support atheistic models of life's origins, is simply being ignored, covered up, not reported... Yet this issue, I think, is absolutely vital to people arriving at the truths of the unseen aspects of the reality in which we live. That these things are NOT true (evolution and it's theories) is shown by the evidence (if we're allowed to see it), and thus mankind is left to wonder... if the evidence is NOT supporting these theories, then what DOES it point to. And the answer is clear: A rational, super-intelligent Designer has magnificently created all of life, and at once. No other theory holds up to both reason and evidence from first to last.
The arguments of St. Thomas, and also I believe metaphysics is a field that deals with some of these things... those truths and arguments are necessary. But naturally speaking, we know everything that we know through our senses. Even Faith comes through hearing. And it is absolutely an error to say that man cannot arrive at definite knowledge of God by reason and by the evidence of his senses. Even if we can't see God directly, we can see evidence of Him everywhere. So questions of science are perhaps much more natural and easier for people to deal with than questions of faith or pure reason.
The minds of men today are just at sea. The larger part of humanity is virtually schizophrenic. They are, in a very real and actual way, getting more and more genuinely out of touch with sanity, reason and reality. For instance, they sincerely think that they can believe all kinds of conflicting things to be actually true at the same time. How can you argue from points of pure reason, against a mind that can sincerely convince itself that 2+2 can and does not ONLY equal 4, but also it can, and REALLY DOES, ALSO equal 8 and 46 and 93? It's a silly example, but in principal, that's how many minds are working today. "Your religion is fine and true for you, and the other people's religions are fine and true for them, and my atheism is fine and true for me. But all of these things are no better than one another. They're equal." That's insanity! You can't really think that all kinds of conflicting ideas can be in any way equal or equally true! But the majority of people alive today do these kinds of mental gymnastics all of the time, as matter of course. (Example: Political correctness.)
I can't really think of too many resources for arguments that are somehow purely in the mind. But I suspect it's because, unlike modern man would like to think, GOD is NOT purely in the mind. He's not a fantasy or an idea. So immediately, when you begin taking Him seriously or talking of Him as part of this reality in which we live (as He truly is), people will automatically go into the familiar realms of that same reality to find out if He is or not. The topic quite naturally turns to everything we know by our senses. There's hardly anything that's quite so universal as the atheist's "show me!" or "prove it!"
Another problem is, because of this schizophrenia in the mind of modern men... this ability to accept all ideas as equal or equally possible or true... they cannot very easily follow any rational arguments like the necessary foundation of human morality in something above and outside of themselves. You can lay out the argument, but in minutes, you've lost them. Because they don't really want to know the truth. The truth that there IS a God, Whom we MUST obey or else go to hell... that's not pleasant to those who don't want to have to obey anyone or anything but themselves. So if you take an intellectual argument such as, to point out that without God, there can be no real morality of any kind... People can't follow it. They don't WANT God, so they cannot follow that kind of argument. Imagine if people even entertained the thought today, that they may be held culpable for the way they've lived their thoroughly immoral lives! Their consciences would eat them alive! They cannot stomach the idea that they cannot just do whatever they feel like doing, because they have been taught all their lives to do just that. Now that they have done just that, their minds just switch off and revolt violently against any "mere" idea or proposition that supports the fact that they have done anything wrong. And so the morality argument which strongly suggests that either there is a God or else we're in big trouble... they can't follow it. It would be searing acid on their minds and hearts and souls to begin to entertain such thoughts.
The only thing they can bend to, are things so evident in the sight of everyone who looks at them, that there is no rational escape. In other words, the hard, physical evidence and it's undeniable implications. And even then... just look how hard they've tried and how long they've tried to deny and avoid what the evidence really does say! They won't admit the truth even when it DOES hit them in the face via the hard evidence. They simply lie, lie, lie... to themselves on the first place, and to everyone else, so that they can go right on denying the God they desperately don't want to believe in. That blindness is something there just isn't any getting around, if the person is truly determined to hold onto it rather than face the very painful (for them) truth.
If you want more resources for the natural arguments about the Creator, I can probably dig up some more of those (I have many, because I've spent many long hours debating it myself), but... chiefly those I've already given are just wellsprings of information. But the evidence is growing toward the truth about God and Creation, and if you can get a bunch of it into a pile and present it to someone who really has got an open mind... the evidence is pretty overwhelmingly in favor of God and Creation, and pretty overwhelmingly against what the atheists would like to think.
Signature in the Cell should be VERY important to the natural arguments, especially, because I believe that book is going to go into the fact that there are things at work in human development and in biology in general, that go even beyond DNA. DNA is only one piece of the puzzle, but recently the evidence has come up to light, that DNA does not do everything or is not responsible for everything people thought it was, or that evolutionists have absolutely depended upon it being responsible for. There are other, mysterious things at work here, and some of the key mechanisms of evolution's theories have been pretty much hopelessly debunked by the discoveries in the field because of it.
Very interesting to read about anyway. But it's the approach that, again, I would strongly recommend. Because of the condition of minds and hearts today, and the gross, rank repugnance for the very idea of there being a God that is in many people... it's nearly impossible to argue from reason, because they would much, much rather run with open arms into any realm of insanity than to face such a truth. Hard evidence is almost the only way with such people. And prayer that they may receive the grace of understanding and acceptance, of course.