You will need a camera that allows you to make time exposures with a bulb setting and a tripod. Unfortunately, many of the newer cameras and digital cameras do not offer this feature.
Meteors are also easy to image.
Again you will need a camera that can take time exposures and a tripod. Just point the camera at the radiant point of the meteor shower and open the lens for 5-10 each exposure. The best equipment you can have to image meteors is a wide angle lens and a viewing site with dark skies. Camcorders can also make nice images of the brighter meteors if you have a dark viewing location.