This type of photography can be demanding. Look for a camera that offers the user easy access to manual settings. Manual focus, shutter speed, aperture, and ISO (sensitivity to light) are important manual adjustments. Optical zoom is preferred over digital zoom. Many members here have commented that a time exposure (need the manual settings) is the best way to get good beam shots. You should also have some way of stabilizing the camera, at least a cheap mini-tripod.
ISO - Try to keep lowest setting possible as high ISO speed can give very grainy result.
Aperture - This controls depth of field (how deep of an area is in focus, in front of and behind focal point)
Shutter Speed - High speed lets in little light, but reduces effect of camera shake. If using slow shutter speed, you want to be on a tripod. Slow speed lets camera capture the beam.
Manual Focus - Lets you preset the focal point in the photo. When you turn out or turn down the lights to take your photo, manual focus will not change. Autofocus may change itself when you turn down or turn off the lights.
Try to find a camera with these manual control options as they add a lot of power to the laser photographer's arsenal. I realize that I am not giving you a brand name here, that is because once you have the features available, it's a matter of practice. Try different settings, if photo is dark, adjust to let in more light. (Slower shutter speed, Higher ISO, Larger Aperture) If photo is overexposed, do the opposite and let in less light.
Many cameras offer "white balance" adjustments. This can be key to getting accurate color that doesn't need lots of reworking in photoshop. Try the different white balance settings out, find what works for you.
Find a brand whose controls and menu structure you can live and work with. Most brands have similar features, but ease of access to the manual features can vary greatly.
Hope this helps ...
Bill.