I have a couple grammar questions. What is the correct punctuation to introduce a list? As in the sentence, "For my niece and nephews: Amber, Luke, and Levi." Would it be a colon? Or is there a more...

I have a couple grammar questions. What is the correct punctuation to introduce a list? As in the sentence, "For my niece and nephews: Amber, Luke, and Levi." Would it be a colon? Or is there a more elegant way?
Also, can you explain the rule of whether to put end punctuation inside quotation marks or outside? I find it very awkward to place it inside when the quotation isn't itself a sentence, as in, "The sign says, 'Stop.' " I 've been told that's the correct way, but it seems bizarre to give a stop sign punctuation.