Brushing your teeth alone cannot remove the plaque trapped between your teeth. The only way to properly clean your teeth includes brushing and flossing.
Brushing your teeth removes the film that builds on your teeth called plaque. If plaque is not removed, it eats away tooth structure causing cavities
Anything with fluoride! As long as you find toothpaste you like and brush properly, any fluoridated toothpaste is acceptable. Be careful about those with baking soda and some whitening toothpastes, because they can be abrasive and wear away your teeth and gums if one brushes too hard.