Based on my experience with several banks, sharing my personal views.
Basic needs should have
Zero balance account
Easy account opening procedures
Zero/Low Maintenance charges
Good support
HDFC - Largest private bank in India, more no of ATM’s and good online portal, Mobile app and good support.
SBI - They have an exclusive option for Corporate Salary Package which offers wide range of privileges.
Axis Bank - They have varied offering depending on the salary slab. Some features like Personal Accident cover, Zero Lost Card Liability are attractive.