You can Go with Kotak 811 it's a good bank account with almost zero charges for most of the service a student might need. Else, another good option is ICICI Bank Campus power variant. Also in digital space there are some new age bank account but not as reliable as traditional banks due to various reasons.
Well if you go with hdfc. They will offer you pre-approved unsecured credit card after 3-4 months which is fastest I have seen.
Standard chartered zero balance savings account is also a good option as they don't change any fees even for their platinum debit card..