You can try POSB or DBS, both offers a basic savings account that comes with an ATM Debit Card. There's no difference between the 2 banks btw, they are the same company. So you can use your POSB ATM Card at a DBS Terminal and vice versa. The terms offered by both banks are similar. No minimum deposit however there are some fees involved below:

Fees

S$2 fall-below fee if the average daily balance falls below S$5,000.
S$20 early account closure fee if the account is closed within 6 months.

However, since every mother/son/father/etc.. has a POSB/DBS account, ATMS and the banks can get crowded. You can also do a check on UOB or OCBC.