What are some good work-outs for weight loss?

I'm 17, 5'7", and about 225lbs. I am a vegan, which clearly doesn't make you skinny, as I am not. I would really like to lose weight and get stronger. I have never really felt pretty, but it doesn't bother me. I would really just like to be able to hike and climb and do fun, out-doorsy type things. Even the things that I'm able to do, I don't do in front of others, as I have always felt self-conscious. I would like to know some exercises I can do to get rid of lower-belly fat, arm fat (whole arm,) calf fat, and neck fat. Thanks for the help.