I can give you several.
1. When one seriously considers the logic of the existence of God (theism), the arguments for his existence are far stronger than the arguments against. These are arguments from causality, purpose, design, fine-tuning, morals, language, and ontology. While all the arguments for the existence of God can be argued against, they make substantially stronger cases than arguments for atheism or scientific naturalism. Those arguments are factors of reason, not faith.
2. When one seriously considers our natural world, a full assessment of what we see in consideration of what it's like and how it got there is much more agreement between theism and nature than between atheism/naturalism and nature. These are factors of reason, not faith.
3. When one seriously considers the contents of the Bible, one can see many examples of corroborated historicity, writers who cared about integrity, and an effort to give people a worthy model of how to live (ethically, honestly, the love toward others, etc.). Those who denigrate the Bible usually do so on its theological claims and its declarations about miracles. Those are believed on other bases founded on evidential grounds and logical progressions. But as far as the Bible itself, aside from its theological claims, the text can be counted on as a reliable historical and cultural record.
4. The person of Jesus. While little about his life can be corroborated by extra-biblical sources, the main parts of his life can be established. On the basis of historical sources, there is no reasonable doubt that Jesus existed as a man. He was a Galilean Jew who was born between 7 and 4 BC and died between AD 26-36. Most scholars hold that Jesus lived in Galilee and Judea, did not preach or study elsewhere, was called Christos in Greek, had a brother named James, and that he spoke Aramaic and may have also spoken Hebrew and possibly Greek. It is believed even from non-Christian sources that he had both Jewish and Gentile followers, and that Jewish leaders held unfavorable opinions of him. Although there are great differences (outside of the Gospels) trying to reconstruct the details of his life, the two events whose historicity is subject to “almost universal assent” are that he was baptized by John the Baptist and shortly afterwards was crucified by the order of the Roman Prefect, Pontius Pilate.
On the basis of these factors involving logic, reason, evidence, and corroboration, I find the God of the Bible to be rationally justifiable.
In addition, I consider faith in the Bible to be grounded on evidence. In the Bible, faith is all about evidence. God appears to Moses in a burning bush before He expects him to believe. He gave signs to take back to Pharaoh and the Israelite people, so they could see the signs before they were expected to believe. So also through the whole OT. In the NT, Jesus started off with turning water into wine, healing some people, casting out demons, and then he taught them about faith. And they couldn't possibly understand the resurrection until there was some evidence to go on.
When you read the Bible, people came to Jesus to be healed because they had heard about other people who had been healed. They had seen other people whom Jesus had healed. People had heard him teach. Their faith was based on evidence. Jesus kept giving them new information, and they gained new knowledge from it. Based on that knowledge, they acted with more faith. People came to him to make requests. See how it works? My belief in God is based on my knowledge of the credibility of those writings, the logic of the teaching, and the historical evidence behind it all. The resurrection, for instance, has evidences that give it credibility that motivate me to believe in it. My faith in the resurrection is an assumption of truth based on enough evidence that makes it reasonable to hold that assumption. Jesus could have just ascended to heaven, the disciples figured out that he had prophesied it, and went around telling people He rose. But that's not what happened. He walked around and let them touch him, talk to him, eat with him, and THEN he said, "Believe that I have risen from the dead."
- In Matthew 8.4 Jesus encourages the man he just healed to go show the evidence that it was true.
- John 14.11 (and also 17.8): Jesus encouraged people to verify the evidences
- Heb. 11.1: Faith is based on evidences
- Romans 1.20 (the passage you mentioned). There are evidences, and we shouldn't be afraid to investigate them.
The parts of the Bible that I believe, then, are because the evidence under them is so substantial, and theism is so rationally justifiable, that it's a very small step to believe the Bible's theological claims and its affirmations of miracles.