Peter Kreeft has a fine site that includes some of his apologetics. The following is a good starting point for an argument for the existence of God:
Before we answer this question, we must distinguish five questions that are often confused.Source: Can You Prove God Exists? by Peter Kreeft
I believe we can answer yes to the first four of these questions about the existence of God but not to the fifth. God exists, we can know that, we can give reasons, and those reasons amount to proof, but not scientific proof, except in an unusually broad sense....
- First, there is the question of whether something exists or not. A thing can exist whether we know it or not.
- Second, there is the question of whether we know it exists. (To answer this question affirmatively is to presuppose that the first question is answered affirmatively, of course; though a thing can exist without our knowing it, we cannot know it exists unless it exists.)
- Third, there is the question of whether we have a reason for our knowledge. We can know some things without being able to lead others to that knowledge by reasons. Many Christians think God's existence is like that.
- Fourth, there is the question of whether this reason, if it exists, amounts to a proof. Most reasons do not. Most of the reasons we give for what we believe amount to probabilities, not proofs. For instance, the building you sit in may collapse in one minute, but the reliability of the contractor and the construction materials is a good reason for thinking that very improbable.
- Fifth, if there is a proof, is it a scientific proof, a proof by the scientific method, i.e., by experiment, observation, and measurement? Philosophical proofs can be good proofs, but they do not have to be scientific proofs.