I'm with everyone else in "spreading your wings", Ethan.
Don't be too quick to dismiss the "religious" schools. My stepson is currently going to a prep school that's very strong on faith, but it's all faiths. It's very open religion-wise and teaches the kids to respect each other's religions, and he's getting a great respect for the moralities that all faiths provide. He really hasn't picked up a faith or religion or anything for himself yet, but none of it bothers him at all. It's actually done just the opposite, it's made him want to learn about the religions to see what they're about.
It's definately had a positive impact on him. I don't know if he'll come out of it all with anything for himself aside from knowledge of the ideals of the different faiths, but as his step-parent, and someone who loves him very much, and someone who knows how these ideals will give him peace and confidence as he moves out to college and beyond, I couldn't be more pleased.
If the schools are going to hold you down and tattoo you and staple a hat on your head, I'd definately lean away. But don't discount them directly on religious affiliation, look at their numbers, placement, ratings, etc.
Pick the best school.
You'll do great. Take this to Dad, too. I'm sure he's got great input for you.