I think indian banks are the good option to open an demat account they
provide below mentioned benefits
1.Shares Can be Transferred Immediately though demat account
2.No Stamp Duty on Transfer of Securities
3.Earlier, individual shareholders could not sell share with odd lots,
it is possible now in India
4.You can now nominate individuals when opening a demat account
I would like to recommend you do not go for private financial
organization.
You can open demat account in following banks
1. SBI bank
2. Indusind bank
3. HDFC bank
4. Bank of Baroda
5. Central bank etc