So this rediculously complex web they've made of 4th edition and essentials is way over board. I think however now that I have a firm grasp on it.
Starting off as a brand new player (with 0 RPG experience) or getting brand new players into the game, what you need is the Red Box. The alternative is the free introductory adventure. Personally, I would go with the free introductory. Though to be fair I would hold off on 4e if you haven't started already. Fifth edition (Or, Next) is coming across the horizon and looks great so far.
For the returning player, the Player's Handbook is the way to go. The alternative is Heroes of the Forgotten Kingdom or Heroes of the Fallen Lands. The difference is the Heroes books are paperback, cheaper and contain the most up to date rules, BUT only half of the races and classes. Plus the classes are have little to no customization. If you get the heroes books, you will need both of them, which will cost more than the PHB. Getting the Player's Handbook will save you some trouble down the line. The rule differences are (mostly) covered in the rule errata.
Moral of the story? Essential books are not essential. Nor do I advise them EXCEPT the rules compendium. Beyond that, as a DM the other material will expand your game (DM Kit, etc). Moral of the story, get the good old stuff.