At All India Rank of 35k and NEET Score of 570 you should target both of the Government as well as State Medical College Counselling. I believe at 570 you have a better chance of securing an allotment in the best Medical Institute of your state. Do keep a check on the Counselling Date and Procedure.

For more information and college prediction do follow the link below

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer