If you're a new DM, I recommend not getting lots of expansion books for a while - they'll just make your life more complicated. The Dungeon subscription is a good buy; I would also consider subscribing to Dragon - there's a lot of good stuff there, too.
Dungeon Master's Guide 2 has a lot of good advice that seems ideally suited to new DMs. Or you could pick up the .pdf of the "Campaign Sourcebook and Catacomb Guide" from Paizo.com - it's for 2nd Edition, but has no mechanics in it whatsoever, and represents one of my best buys for DMing advice.
I would recommend the Shackled City hardcover, which compiles the first Adventure Path from Paizo. My group spent a year running through this, and it is an excellent campaign.
The Forgotten Realms Campaign Setting book is excellent. Alternately, if you prefer, there's the Eberron Campaign Setting book, which is also good, if that's more to your taste, although I didn't find the book itself as well put together. There are other settings out there, but I can't speak to their quality as I haven't checked them out.
Beyond that? I don't know. There are a wealth of books out there, and a lot of good books. However, I'm not sure they'll actually improve your game experience - in general, I recommend that new DMs use just the core rules for a while. However, if you are determined to go ahead, the ones I would recommend are the Players Handbook 2, Lords of Madness, Fiendish Codex I (this will be rated higher once volumes II and, hopefully, III are released), Spell Compendium, the Expanded Psionics Handbook (if you like psionics, of course) and Unearthed Arcana, in that order.
Edit: Forgot the Spell Compendium!