Weight doesn't matter, and you're the same height as me. I ride a Triumph Bonneville T100, but you can ride anything you like. The best thing is for you to sign up for the motorcycle safety foundation basic rider course. There are chapters in all 50 states, and they will provide all the required equipment including the motorcycle. This way, you can ride a little bit and see if you like it. No prior experience is required. They assume you have never even sat on a bike before, and many people in the class are in the same position as you.
The most popular first bikes are 250cc bikes like the honda rebel, yamaha virago, and ninja 250. Used is best for the first bike, since we all tend to slip and drop the bike at least once when we start riding.