Ask your dentist to recommend a toothbrush. Depending on the state of your teeth and gums, she may give you a soft-bristled regular toothbrush or steer you toward an electric one. Always get soft-bristled brushes or heads to avoid pushing gums up.
Get a buzz with vibrational toothbrushes. They work better because people brush longer and more debris is loosened by the vibrations. Many dentists recommend the Philips Sonicare Elite with its curved head, great for getting around the back of the teeth and for powerful, gentle cleaning at the gumline.
Buy an electric toothbrush with a rotational oscillation design; although it costs more, it gives you tangibly better results. An example of this is the Braun Oral-B 3D Excel, which has bristles that spin in two directions.
Experiment with tufted, angled or rounded-end bristles and easygrip, curved or flexible-grip handles to see which type of toothbrush best helps you reach the nooks and crannies.