Usage of 的 to refer to a generic class of things
Short answer: yes. Your understanding is mostly correct.
Long answer: what happens in a sentence like


  我喜欢吃好吃的 
  I like to eat delicious things


is that you are omitting something that would otherwise appear after 的. In the example above I omitted 东西。
This omission is fine with very generic nouns. I can come up with the following:


东西 (material thing): 我喜欢吃好吃的[东西] I like to eat delicious [things]
事情 (immaterial thing): 我不喜欢复杂的[事情] I don't like complicated [matters/stuff]


You can then omit any other non-generic noun provided that what you are referring to is known from the context. 


  你回来的路上能帮我买一些苹果呢？我不要大的。
  Can you buy me some apples on your way back? I don't want the big ones.


If it is not easily understood from context, than you should specify the noun, as in: 


  我喜欢可爱的东西
  I like pretty things.


To make up a rule of thumb, just remember that you are omitting something. If you can convince yourself of this, it's easier to distinguish between noun phrases with an omitted noun and regular adjectives. 
In your examples above:


不要大的 -- noun phrase with omission -- I don't want the big one(s)
不是大的 -- adjective, with 是 for emphasis -- It's not big!
不大的 -- adjective with end-of-sentence 的 particle (expresses certainty) -- It's definitely not big!
不大 -- negated adjective -- not big


Therefore, the correct way to colloquially express the adjective + omitted noun is by preceding it with a verb, just as if it were a normal sentence.