Essentials first. See my
initial impressions, but I'll expand my thoughts here now that I have a few months experience.
Rules Compendium: It is the most comprehensive and up-to-date version of the rules. A fantastic product that I recommend everyone playing 4E pick up and use.
Heroes of the ...: If your son like his Starter Set characters, I'd lay off for now. Pick up one or the other when you want a rules reference for players, character creation rules that are more streamlined than the Starter Set, and--obviously--different race and class options. I miss gnomes and githzerais and sorcerers and monks and dailies psionics in my current Essentials-only games. Take a long look with your son at the various races and classes in the PHBs and Hot... books before spending any money. Yes, the PHBI has been extensively rules updated, but it's not that bad if you only pay attention to the races and classes and use the Rules Compendium for gameplay mechanics.
DM Kit: Nice. More tokens, more maps, what looks to be a good adventure, and a nice DM screen. Get this if you are going to be creating your own adventures. If you are using mostly published adventures you can wait. If you do get this, take a close look at the DMGI and DMGII later. They are two of the best guides ever printed to creating and running RPG sessions for any system. Also the new DM kit leaves out plenty, while updating other stuff. Probably most notable, the DMGs have monster creation rules that are missing from Essentials.
Monster Vault: A great set of monsters: extremely iconic, extremely playable, and tokens, tokens, tokens. Also has an adventure I haven't looked at very closely. Like the DM Kit, pick this up when you start creating your own adventures, but you can lay off for a while if you're using published. This pretty much entirely supersedes the MMI, but I'd take a look at MMII and MMIII for more exotic fare.
Tile Sets: To answer your question of whether you can just describe a setting and let the players map it in 4E, the answer is not really. You'll want to fill your encounters with interesting features to maximize the tactical nature of combat and add flavor to your settings. When every square matters you can't really leave it to your players to try and guess what you're talking about.
For this reason I've become a big fan of dungeon tiles. They let you quickly lay out the map space as the players encounter it with more verisimilitude than ink on paper. Even if you use paper as your main map, strategic use of tiles can really highlight something unique or interesting in your encounter.
I think the tile sets are very good values, and if you start using them you'll soon want at least a couple of each. I also encourage you to discover Gaming Paper.
Pre-Essentials Books: See
my review of every pre-Essentials supplement. In a nutshell, Underdark and Open Grave are very much worth considering in the Heroic tier. Manual of the Planes, Plane Below, and Plane Above should get a look if you want to venture into the Paragon tier. Player's Strategy Guide is extremely underrated and I recommend it to new players even post-Essentials.
Insider: Get a month and see what you think. I don't subscribe, and have no problem creating characters, adventures, or monsters or running my games. The price of one month is probably worth it just to get the complete archives of the post-DDI issues of Dragon and Dungeon magazine.
Most importantly, don't get bogged down in rules or supplements. Start with your flavor and drama and the core mechanic ("roll a d20" or "make a check" should be the 4E DM's mantra) and end with having fun.