Typically with this sort of a problem common state and behaviors are placed in the superclass. A good place to start would be to create an Account class, and add methods to it to check the balance and deposit money, then add the other (specific, not common) behaviors to subclasses. Something like this:
class Account:
def __init__(self): ...
def deposit (self): ...
def get_balance (self): ...
class CheckingAccount (Account):
def __init__ (self): ...
def pay_bill (self): ...
def withdraw (self): ...
class SavingsAccount (Account):
def __init__ (self): ...
def make_investment (self) ...