Advice to do with 10 lakhs

Hello All, I am getting about 10 lakhs from LIC policy that matures this year, paid my last premium(20 years). This will be my first time investing in India stock market and I am leaning on Index investing. I absolutely have no flair for stock picking. Since I do not plan to touch this money for like 15-20 years I would like to do lumpsum into Index and I may or may not do the SIP monthly so that's a question for another time. I seek advice on below... 1. Bank and brokerage account I need to open (best ones) 2. what proportion should I allot for Large/Mid/Small cap ? 3. Best index to pick in Large/Mid/Small cap ? Thank you.