Here's my response to a blogger who said to a Christian, "the only thing here that is factual is that you have chosen to believe with no evidence."
1. The rise of the early church, with an undisputed resurrection message very, very early on. That's evidence.
2. The uniform willingness of the first apostles to be put to death rather than deny their claims about the resurrection. Some persons may be willing to be put to death for something they believe is true, but few if any are willing to be killed for something they know to be false. Not a single apostle repudiated his witness that Christ rose from the dead and appeared to them. That's evidence.
3. The existence and witness of the four gospels. That's evidence.
4. The words of Christ recorded in the gospels. What they say, especially, about the inward human condition, the human heart. He claims that all men are sinners at heart, falling short of the demands of truth and justice and love. Christ's words can be weighed and evaluated, and one can reach some kind of opinion about him based on his words. That's evidence.
5. The fact that, based both on philosophical and scientific arguments, the universe had a beginning. If there's a Beginning, that is evidence for a Beginner, because in all of our collective human experience, everything that begins to exist has a cause. There are no exceptions to this. So there is certainly nothing illogical or unreasonable about believing in the existence of a Creator. That's evidence.
From that point, it is a matter of making diligent personal inquiry into the nature of this deity, and whether He has chosen to communicate with His creation.
6. Finally, believers enjoy the witness of God's Spirit to the truth of Christ's message. Jesus said that God keeps the secrets of his kingdom from the "wise and prudent", and reveals them unto babes. Christianity is, from first to last, a religion based on revelation.
But that does not mean that it is unreasonable.
There is plenty of evidence to make a leap to faith based on informed reason.