I agree that classic might not be the best term to use here.  You want your thesis to be clear and specific.  I would replace classic with important, because that is really what you mean.  First, focus on the idea of archetypes and connect it to emotions, rather than making those two separate ideas.  How do archetypes relate to emotion?  Then your thesis is on its way.  You just need to follow it up with specific reasons.

Instead of using the classification of 'classic film,' you could designate the movie as being 'iconic' and then provide numerous supporting details about why the film is iconic, starting with your own explanation about what does make a film iconic.

Working the notion of your own criteria for "classic film" into your thesis statement will help to deal with the suggestions you have received above. Without making the essay subjective, you can work to define a set of criteria for what you think makes a film a classic and attempt to prove that this film qualifies. 

Your current measures of the film are very different from your initial ones...I might recommend going back to your first ideas, as they are more cinematically oriented than the latter ones. 

The first problem you face is to define "classic film." There are two concepts of this term abroad. Most commonly know is the colloquial, or everyday, meaning, and it can describe anything from a well liked film to Bobby's favorite new cult film. The second definition is an academic one and was developed by Bordwell, Staiger and Thompson in Classical Hollywood Cinema. They define classical film according to:

1. time period (1917-1960),
2. narrative structure,
3. editing characteristics,
4. unified, linear cinematic space and time,
5. unifying style in motivations and conventions.

I suspect that your assignment draws upon the colloquial definition as referenced in the question: "How is this a film classic to you?" In which case, your second thesis topic (post #4) seems a good one to me.

The term “classical” film implies that some cinematic rules or guidelines were followed in making the film.  Your thesis statement is a little too vague to make a strong argument for “realistic characters dealing with emotional themes”.  Do these criteria fit other classical cinemas, for instance Wizard of Oz or Psycho or Rear Window?  For one thing “realistic characters” does not fit a film with an angel and a hero who goes backwards into his life, etc.  For another, these characters are not so much emotional as they are stereotypical.  If you want to make a thesis statement that allows you to discuss this movie, you must venture an interesting or controversial viewpoint worth defending with detail.  How about “this film is not a Christmas classic, despite its ending”—you could use Miracle on 34th Street as your contrast, and argue that It’s a Wonderful Life is only Christmas-y in passing, but is really about money.