Okay - so this is a complicated question because I don't know your age or exactly what's bothering you.  Sun damage has a lot of different problems it can cause.  It can make the skin brown and blotchy, it can cause those tiny red blood vessels (telangectasias) or both.  The brown spots plus that network of reddish vessels is sometimes called poikiloderma.  It can also can wrinkles and loss of elastic fibers in the skin which shows up as sagging.

 But..... I'm going to guess that what's bothering you on your hands is brown spots in which case the IPL or Fraxel Dual would be best.  There will be a new article soon on the Fraxel Dual.  

On your chest, it could be brown, red, or wrinkles so it's a little harder on this one.  Also, age plays a role in the decision of which laser will be most cost effective.  I need a little more info to answer this one.  The LED rejuvenation might helpful for maintenance but it's not going to be cost effective if you already have damage.    Dr. I