So your parents are entering on a lottery GC? They can afford to live in the US and get health insurance? But not work? Did you state how long they have been absent from the USA?? And you too. You should pay attention to how absence will not only affect reentry but your path to citizenship. If citizenship is a priority pay attention to how GC holders are being subjected to protracted waiting periods, reentry scrutiny and deportation for seemingly arbitrary offences.