I prefer to look at the saga as whole, as I always have - but I can separate the trilogies for the purposes of debate.
Since I was one month old when the first movie came out I can say that there was no 3 year period of me thinking that Vader literally killed Anakin. I barely recall seeing Empire in the theater and I do remember seeing Jedi, when I was six.
Whatever the plan was, whatever was in an original draft doesn't matter to me. What does influence my opinion is what was actually on screen. From the very beginning, Vader and Luke had a connection beyond the fact that Vader supposedly killed his father. Foreshadowing is a wonderful tool and it is used subtly through the interactions of Vader and Obi-wan and their master/apprentice relationship. This relates to Luke directly and is revealed in the trench run at the end of the first film.
You can slice up the narrative as simply being about Luke's adventure to defeat evil but I believe that is missing the heart of the films. Star Wars is a special animal because it lends itself very well to serialization and additional stories. This was done on purpose. You could tell, without even having to know that Lucas was planning more films (or just by paying attention to the Episode VI tag in Jedi) that there was more the Luke saga which included Anakin, Obi-wan, Yoda and the Emperor.
In Star Wars: A New Hope, we meet The Hero (Luke) and his companions. Darth Vader is X-factor at this point as we are lead to believe that Tarkin is the main villain of the saga where he really isn't (that would be Palpatine). A New Hope is easily Luke's movie, and it has to be for the character to make any sense. We Vader as an antagonist but know there is more to this character than we are being shown, because it is Luke's movie and it has to focus on him.
In Star Wars: The Empire Strike Back, we still see our hero and his companions but we are introduced to the mastermind, Palpatine, and see much more of Vader in action. We are also introduced to Yoda, the last remaining creature alive who can teach one in the ways of the Jedi: the teacher figure to take over for the dead Obi-wan, who's role must be filled. We learn that there is even more of a relation between Luke and Vader over the course of the film and then at the end it is brutally confirmed. Here is where we see that Anakin has fallen and is continuing to fall.
Star Wars: Return of the Jedi brings us the redemption and the completion of the cycle to which we are missing the rise of Anakin. Leia is revealed as being much more than we thought she was in the fact that she is a Skywalker. This lends itself well to further serialization as you could see Luke and Leia trying to fix what their father did (which is debatable). We see Vader finally do the right thing and see a bit what he was like as Anakin in his love for his son.
So there is a good amount going on in all 3 films but it boils down to Anakin's redemption, which is spurred on by Luke and his belief in his father. The only way this works is by Vader redeeming himself by killing Palpatine and becoming Anakin once more, which kills him - he sacrifices himself for his son and the greater good. The redemption happens at the very end, but it is at the heart of the story. A man's soul is saved and good wins the day.
No where in there is any material from the prequels. There is something to be said for each movie in the original trilogy building on and making the previous film(s) better and more robust - which just happens to hold true for the prequels as well.
I think too many folks focus on what writers, producers and directors say should have or what originally was supposed to happen in plots. I'm all for that but I find it's best to go on the actual product for purposes of debate concerning story.
So, Star Wars is many things. It is the story of a hero defeating the ultimate evil. It is a war story that focuses on a small group of people aiming for the same goal. It is the story of 2 people finding each other amidst the chaos. But it is ultimately about redemption which is the theme of all three. Without redemption, Han doesn't come back to save Luke's bacon, Yoda doesn't train the one person who will reach Anakin, Lando doesn't blow up the second Death Star, Obi-wan doesn't help obsolve the biggest failing in his life and Anakin doesn't kill Palpatine.