While the foremost point of concern is the interest rate offered, you should also learn how to choose the right fixed deposit rate. This depends on your needs too. If you need monthly returns, the interest earned may be slightly on the lower side. You can leave it as a cumulative deposit where interest is reinvested with compounding benefits if you can wait till maturity.
Whether the bank offers an interest rate to meet inflation should also be a factor for consideration.
Compare the fixed deposits offered by various banks with an FD calculator and then decide on the right rates.
You should know if the bank is flexible for premature withdrawal of deposits in case of any emergencies and also the penalty charged for the same.