So, this is an interesting dichotomy.
The PHB does a great job of introducing people to the game, especially the 2014 version. It goes in detail what each thing is and introduces them to each item. What is a race/species. What is a class. How do they work. etc.
It's also a lot of reading. However, that's the type of detail you need to introduce new players many times.
On the otherhand, a Starter Set (as opposed to a Basic Set or Beginner Box) should be made so that you can just sit down and play.
First item...Everything is on the board to begin with. You don't need to select cards, you don't need anything else except to select a Character/board. It is all there. You don't have to do any other reading to create your character, you have it there already.
Then you have an introductory adventure that is on the rails. This takes the DM and players step by step through each of the new rules and items. They get to play as they are introduced on how to run and how to play the game.
This is what goes into the Read Me First booklet. If not that book, then a Read Me Next Book. The Read Me first book in that instance would be to show a picture of the Player board and to tell them to get one of these boards. Then it would explain that this is their character and to have it in front of them. It would give an example of Roleplaying that is around a page long and then guide the DM on leading that exact scenario (it would only be one scenario) in which they learn about what spaces are and how to move (or something simple like that). It would be a very guided scenario.
Then the Read Me Next would be an Adventure on the Rails where it introduces a new concept in each scenario within it (for example, this is your attribute scores...lets see what a use for them can be).
Sort of like they do in some of the Good Video Game tutorials or other things today.
Finally, AFTER they have read the Read Me First and Read Me Next booklets and book (which will be several dozen pages or more, just in themselves) you can have a proper Rulebook and Module (similar to what they included in their Starter Set already). You could even include another Blank Player Board or one that they can modify (similar to what is now included in the Starter set) so that they can make their own characters and such.
This accomplishes the goal of getting players to play almost immediately on sitting down and getting them involved with play (which is one of the reasons and designs of the Starter Set) while also introducing them very easily into the rules (another goal of a good Starter Set).