The "proofs" of God's existence are probability arguments. I mentioned earlier the argument that uses the beauty and order in the universe. We have to decide if this is a product of random processes or due to the directing influence of a creator. Everyone has to decide for themselves what conclusion they draw. As mentioned above by Craytonoics, the five most important arguments are to be found in the Summa Theologiae (St. Admin Aquinas, not St. Augustine). All of them are not "proofs" in the modern, scientific sense. They give evidence for God's existence, but not conclusive evidence.
It was said earlier, that the idea of God has been made up so that people could feel happy. I am not sure which religions have ideas of God that make people feel happy, but I am sure that this is not the case with the Christian idea of God. The Christian God sets up strict rules that He wants mankind to obey. Life is much easier without God. But if you are convinced that there is a God and that your (Christian) ancestors did not lie to you, then you have no choice and accept His rules. One thing is for sure, death is much easier for believers than for atheists.
The problem of evil was brought up several times, but I don't think it was really discussed. Unfortunately it is not so simple as to say: Evil exists, therefore God does not exist. I could turn it around and say: Good exists, therefore God exists. Neither argument holds. The problem of evil has been discussed for many millenia. Christianity's answer is very simple: Freedom. Freedom is the much higher Good than preventing evil. God wants us to be free and freely decide to believe in Him. This also means to allow us to make the choice of evil.
As my last point I would like to discuss if Christians are better than Atheists. To say itup front, I do not know the answer to this. What I know is that I am a better person because I believe in God. And I think this is the case for many others as well. Let me give you an example. These are the thoughts that someone had on March 30, 1981:
"I looked on that tiled ceiling and prayed. But I realized that I couldn't ask for God's help while at the same time I felt hatred for the mixed-up young man who had shot me. Isn't that the meaning of lost sheep? We are all God's children and therefore equally beloved by Him. I began to pray for his soul and that he would find his way back into the fold."
I have been in similar situations, not as serious, nobody ever tried to kill me. I remember situations where I calmed down and forgave someone becaue the line from the Lord's prayer came to my mind: "Forgive us our trespasses as we forgive those who trespass against us". President Reagan must have thought of this very line on this day in March of 1981.