Well, the non-denominational and modern part gave me a great chuckle. We strive to be non-denominational, but modern wasn't on the mission statement, but I guess you can say that. I want this place to feel up with the times. ;)
I had a good friend in college who grew up with one Jewish and one Catholic parent so I've definitely heard about the split backgrounds. We try not and get too denominational around here, but it's not a black mark to be one way or another.
Actually reading, studying, and working with God to understand is the single most rewarding thing you can do when it comes to the Bible. If you stick to it, it most certainly will influence your relationship with God.