Variables have scope, so yes it is appropriate to have variables that are specific to your function. You don't always have to be explicit about their definition; usually you can just use them. Only if you want to do something specific to the type of the variable, like append for a list, do you need to define them before you start using them. Typical example of this.
list = []
for i in stuff:
list.append(i)
By the way, this is not really a good way to setup the list. It would be better to say:
list = [i for i in stuff] # list comprehension
...but I digress.
Your other question. The custom object should be a class itself.
class CustomObject(): # always capitalize the class name...this is not syntax, just style.
pass
customObj = CustomObject()