On what evidence, if I may inquire?
Well it's a long story, may be we'll go into more details as the debate goes, but basically I worked it the other way around. Not start by the "unclear things", but rather the broad lines, the main things.
For me, it doesn't sound logical that there is no creator for the universe. You can say all you want about the scientific theories, but in reality, they're all only trying to explain what could have been the mechanism for the creation, or how things work. It's like seeing somebody shot by a bullet, and when I ask you who did it, you tell me, well there was a small explosion inside something called a gun, which lead to big pressure that pushed the bullet at a very high speed, and eventually hit the man. Ok, yeah, but who pulled the fecking trigger? Personally that was my thought process.
Religions (Abrahamic religions) are the only available source that provided me with a logical answer. Somebody, or something named God.
Now those different religions, as much as they differ from each other, do give you the feel that they belong to the same source, especially when you read the book of the last one (Islam), and you see that it acknowledges indeed that they were all from the same source. "God".
Then I started to think about other things, logically. For example, God can't be materialistic, otherwise he's just part of the universe rather than the creator of it. And if God isn't materialistic then God can not be seen. It makes sense. Things like that are also explained in the Quran.
Then when I read it, it actually made sense to me (especially the parts that were easy to understand, including the things it asked the people to do), and it provided me with answers nobody else could provide me with (like what happens after we die, why was Earth created, why don't God just show us himself in some way so we all become believers, why doesn't he force people to become believers, why does God allow bad things to happen on Earth...etc.) and all the answers made sense to me. The Quran is also supported by historical facts from that period and historical facts from other periods, that convinced me that it's very unlikely that it was just a "crazy man making stuff up".
There is of course more to it, but that's basically how I got there.
Also all the "evidences" that "prove" that the Quran is wrong, can be easily answered, especially if you have a good grip about the Arabic language (even though they might not be easy to explain fully).