You sound like you are what we call skinny/fat. Even though you are at a relatively low weight you have relatively high body fat. That is why things like height/weight charts, BMI and girth measurements that do not take into account your body fat level are not very good indicators of health and fitness.
Everybody is different, but generally resistance exercise coupled with a clean diet is better for reducing body fat, although some people for either genetic or psychological reasons find cardio better suited for themselves. Remember the best exercise is the one YOU will do consistantly for the long term. If you are up for it a combination of alternating days of resistance exercise and cardio also works good for many people. The cardio does not have to last longer than 20 minutes or so to be effective.
Clean diet means as little processed foods as possible. Stick to protien sources (meats, eggs, nuts, dairy, etc.) and fruits and vegetables whenever possible. Some people can tolerate moderate amounts of starchy carbs (grains, breads, pastas, cereals, white potatoes, etc.), but if you are trying to reduce body fat you may want to limit or avoid them until you reach your goal.