Well if you guys are planning to dye your hair on a consistent basis, you have to make sure that you select the right product to start with. Because over the passage of time, if you have selected a cheap product, it might start the damage your hair.
If you have dyed your hair just because you want to bleach them again, then any hair damage might not be caused by dying, it would be bleaching to blame it.
If you want to choose a color, you can go to a good shop and have the manager guide you in choosing the right color.
Hair dying is rumored to cause cancer. Well, mostly rumors are not true. But what you guys should do it to make sure that you read the ingredients on the color. If you are allergic to any component, i would advise you to choose some other color.
If, after dying, you notice that you wanted to get them dyed a bit lighter. In that case, in spite of dying them again, you could just let the color on your hair fade a little.