A little of both actually.
I think it is much better to wait until you are ready to learn about all of them independently (when you are mentally & spiritually mature), and when you have a very strong interest, then you should really study all of it with an objectionable view point. I think that will lead a person to a stronger faith and a better understanding of their views, etc.
At the same time, I don't think it hurts to believe in what your parents believe while you are young. I used to believe a lot of things when I was young that I heard from others regarding religion. It didn't hurt me, and I eventually did kinda what you did and just re-examined things for myself. I am still a Christian, but I do have some different beliefs on several topics.
But by examining it all myself when I was ready, I think it made my faith and belief system that much stronger.