Best bodyweight exercises to lose weight and maintain fitness?

I'm severely overweight and addicted to ciggerates. I have developed back and neck pain (more like discomfort) that doesn't go unless I stretch or crack my bones. It's clear I need to exercise since I don't do it all, but I'm too ashamed to go outside because of my weight and because I juggle between home and college too much to justify a gym membership. Really need some tips, I think it's still not too late for me if I start soon.