orcishgamer: D&D Essentials is a money grab with very low quality bindings and paper on the books. There is also nothing new (or very little new, at best) in them. Take a pass on these low quality books, no reason to encourage this poor behavior.
The Red Box is a fun way to introduce new players and is pretty cheap, but is in no way necessary.
Steely_Gaze: I've got to second this. I got suckered into the Essentials line when I got into roleplaying in 2010 and I've regretted it. Low on options, weak on formatting, and cheap as all heck in construction.
I can't vouch for the core rulebooks (I got out of D&D after that experience and moved on to Pathfinder and other games) but I'd definitely buy them before the Essentials.
The core books are better on all counts: binding, paper, and printing. The information is laid out in a more accessible manner (Essentials seems to have been printed for your table's rules lawyer, and seriously, fuck that guy). They aren't even really more expensive. Buy the core books, imo.
KillingMachine: If you're getting into 4th Edition D&D, you should skip the Player's Handbook, Monster Manual and Dungeon Master's Guide. They've all been more or less replaced/updated with the essentials line of products. I'd also recommend skipping the Red Box "starter set" unless you are totally new to RPGs and need some extra hand holding. These are the things from the essentials line that I'd suggest:
Dungeon Masters Kit ( replaces the DM's Guide)
Monster Vault ( replaces the Monster Manual)
Heroes of the Fallen Lands and/or Heroes of the Forgotten Kingdoms ( these replace the Players Handbook)
Rules Compendium ( not totally necessary if you have the DM's Kit, but handy to have for table reference and good for players to have)
maxman43: I agree with this advice.
I cannot express how much I disagree, Essentials is poor quality (see my other posts in this thread) and the information layout is more likely than not going to actually turn off new players.
Barefoot_Monkey: 3rd Edition was actually far more complicated (and needlessly so) than 2nd, but much much better-presented. They both used a perfectly identical equation for calculating hits, but 2nd edition explained it in terms of THAC0, which is very unintuitive (older editions hid the calculations entirely behind a printed table; it took until 3rd Ed before they figured out how to present a simple equation in a simple way). Most of the time you use the PHB only for looking up spells, but only in 3rd Ed were the spells in alphabetical order. Things like that made all the difference.
I think you'd find 4th ed is much more streamlined than even that (if you must have your 3.5 type rules I guess you could do Pathfinder, it's a single book to be a player so your investment is tiny comparatively).
You can finish a fight in 4th ed AND still have time to roleplay in a single 4-8 hour session:)