I have a question for Native Americans/Indians?

I was curious as to what you would prefer being called. I was reading an interview on one of the actors from Last of the Mohicans and she said that she heard someone ask Eric Schweig (who played Uncas) what he would prefer being called, Native American or Indian, he said "Indian". I am very curious as to why. I always used to think that calling you Indian was offensive because it is, after all, what Columbus thought you were; Indians. And you were the first to inhabit the Americas so you would rightfully earn the name Native American. I would really like your feedback so you can correct or support me. By the way, I swear you are the most beautiful people I have ever seen. I went to school in upstate new york in hopes to be in contact with you and learn from you but never saw you :((( Please don't take me in the wrong way. The last thing I want to seem as is a person looking for a trophy or something, I hate and deplore people who do so. Just wish I would have gotten the opportunity to learn about you and get to know you firsthand instead of through movies and books which beat the image of you being people who run around in loin clothes all the time. (Uff, when WILL they stop that) I would very much welcome first hand experiences and stories that you may have to offer. Even the hopes and dreams that you may have for your people. Take care.