There's a few things that Essentials changes if you use the rules from their version of the Adventurer's Vault. Naturally, we'll find out most of them when it comes out:
1) All items are classified as Common, Uncommon, or Rare. This supposedly will also include every existing PHB and AV item, with nearly all of them being classified as Common or Uncommon.
2) A Common item will be found 50% of the time, and is an item that they say 'you apply a stat change to your character sheet, and forget about the item until you replace it'. This includes things like a Belt of Vigor that increases your healing surge, or other items with no daily effects or other triggered things. They sell at 20% base value, and large enough cities will sell them to people.
3) An Uncommon item will be found the other 50% of the time, and is meant for the more complex items that have daily effects, or the like. A Power Jewel, which lets you recharge an Encounter power once per day, would most likely fit into this class. Uncommon items, when sold back, sell at 50% of their value. Uncommon items cannot be purchased without DM permission--and usually purchasing or finding one of your choice is something that creates an adventure, rather than being routine.
4) A Rare item will be found once per tier per character--if lucky. These are a higher class of items, with stronger effects than what current items do--the rarity restriction is meant to overcome the fact that they're noticeably more powerful than another item of their same level, and a character would likely hold onto it for several levels before begrudgingly letting it go. When sold, a Rare item gives back 100% of its value. Rare items cannot, and should not, be bought in stores, and finding one is the culmination of an adventure, or a very lucky happenstance.
5) Daily magic item uses are out the window, as now you have Uncommon items being the items that would use them, and the DM now has control of how little--or how much--he wants to give the players that ability. This does, of course, nerf certain classes (Artificer) if this is used.
The two have the same rule base and are completely compatible.
However, if you are just starting, pick up either or both of the Essentials books Heroes of the Fallen Lands and Heroes of the Forgotten Kingdoms (depending on which classes/races you are interested in. As a DM, pick up the Dungeon Master's Toolkit, the Monster Vault can wait until you have a few games under your belt and are sure you will be continuing. The Rules Compendium isn't needed as all the rules are in each of the Hero's books.
The main problem with the old trilogy (Player's Handbook, Dungeon Master's Guide and the Monster Manual) is that a considerable amount of errata has been issued since those books were released. I'd recommend skipping them until you have the rules well in hand and can grab those books for any options you want.
Best Answer
D&D 4e and Essentals are completely compatible. They use the same rules and same basic ideals.
Looking at this review, as I trust the reviewer, it is better to say that the Monster Vault correctly obsoletes MM1. This is a very good thing, as the monsters in MM1 were, from the perspective of 3 years down the road, poorly designed.
Functionally speaking the only adaptation you will need to do is to older adventures which use poorly-designed monsters.