I suggest making sure you understand the implications and how the immigration system works in the US before making any decisions. It might be relatively quick for them to get there, but I don't know that it will be for you. As far as I know the only reliable way for anyone to become a permanent resident through family ties is marrying a US citizen, or being younger than 21 if your parents get a green card. You can get other relatives in as a permanent resident, but it's a much longer process. There's also the fact that green card applications are not exactly cheap, although perhaps that's different with the lottery. Not a lawyer or anything so don't take my word for it, but be aware that the american immigration system is a confusing mess.
Also I would consider what are they going to do for healthcare, depending on how old they are and what health issues they have. And as you say, what kind of job they will do when they get there, unless they have some other source of income. As someone who immigrated relatively recently, I can tell you that the US are not as great to live in as one would sometimes be led to believe from abroad. Especially right now.
I already decided to not do a PhD in economics and I also quitted my master in economics. Now it will be a second big life decision in a single year. Can my 9 year old sister handle emigration? Can my parents who don't speak English at all manage to earn a living? My work experience in Turkey will be null in the US, though I have a degree from Oxford which should work fine. idk
