Is it good to invest in IDBI.? I want to Invest around 15 Lakhs .?

I am afraid of investing in any private bank . I am not interested in their beautiful offers.
Since IDBI and Andhra Bank are some of leading Public Sector Banks, I wnat to Invest my amount.Please confirm my idea. And also request to suggest any other ways where my money is safe and earns good results and there should not be tax deduction. I am fed up with Govt policies to tax every thing. I cannot pay any taxes.