Well when it comes to the existence of Jesus, many historians agree that Jesus existed, even if they deny His divinity. Here’s one source on that. And considering how Christianity exploded, it’d be implausible for it to all begin because one person made things up in regards to Jesus’ existence. So even if you don’t yet accept Jesus was God incarnate, it’s no stretch at all to believe He existed.
npr.org/2012/04/01/149462376/did-jesus-exist-a-historian-makes-his-case
When it comes to exaggerated stories, the Old Testament does not need to be taken literally. The Church teaches that the old writers weren’t necessarily concerned with getting straight facts across, but meaning. So The Flood for example could be interpreted as a symbol of Baptism. (I’m no apologist so please don’t as for the explanation from me.)
This leads to the view that the Bible is true in all it intends to be true in. As for the contradictions, it’d depend on which ones you’re referring to. Some of the New Testament contradicts Old Testament teachings (like no pork) because Jesus fulfilled the old law and had the authority to make changes. (With pork for example there’s a passage in Matthew where He says “It is not what goes in your mouth that makes you unclean, but what comes out of it.”)
As for existence of God, there are accounts of modern day miracles too, such as Fatima. Others might have more links about those so you can read about them.