Hmm, things to make a Realms game distinctly realms.
1. Organizations. The Realms has a lot of famous organizations/cults/orders. The Red Wizards are the iconic Evil Wizards Cabal with long term plans to conquer the world, the Harpers are a great plot device for PC's to recieve mysterious help, the Cult of the Dragon makes a foe you could base an entire campaign off of thwarting their attempts to create Dracoliches. The Purple Dragon Knights could be brave defenders of the realm, or overzealous enforcers giving freewheeling adventurers a rough time, sometimes even at the same time. The Shadovar are a great reason to bring in Shadowdancers and darkness-themed opponents, as well as a source of any strange magic items or foes who are much like everybody else, but oddly alien.
2. Religions. The faiths of Faerun are another big part of the setting. A Morninglord of Lathander in their bright pastel yellow and orange robes giving prayers at dawn beneath a stained glass window, a Dweomerkeeper of Mystra in azure robes heavily trimmed in silver, wearing a mantle of silver chain netting, or a Watcher of Helm in gleaming full plate, complete with red and white plumes from the helmet go a long way towards making the Realms what they are.
3. NPC's. Yes, a lot of people hate the Realms for its big stable of established and powerful NPC's, but they are a lot of the flavor of the setting. Even a very occasional appearance of a big name can go a long way towards really establishing the Realms feel. The NPC's aren't the stars (a big misconception people have about the Realms), but they make great cameo parts.
4. Realmslore. The Realms has a huge background, and throwing out refernces to major events helps keep the flavor established. An NPC who's brother died in the Tuigan Horde invasion, an obscure reference by an old sage to "Karsus's Folly", a local priest who was blessed directly by his god during the Avatar Crisis (a.k.a. The Time of Troubles). You don't need go overboard on it, but occasional references to these things go a long way.
5. Unlikely Enemies and Allies. Alignment doesn't mean everything in terms of who's your friend, and who is your enemy, politics crosses alignment boundaries. Good can hate good, and Evil can get along with others. The (LG) Purple Dragon Knights could just as easily be a little to overzealous in their defense of Cormyr's strict (but well meaning) laws, turning a typical good-aligned party into outlaws if they forget to get the right permits, the (LN) Church of Helm is far more hated by many in Faerun than even many evil faiths, and the (NG) Church of Mystra has a significant grudge against them (and since both faiths sponsor Paladins, you can easily have two paladins who could fight to the death over their deities). Many evil gods openly accept Neutral, or even Good worshippers (Shar and Beshaba especially), as people pray to them for protection and may even carry their unholy symbols while not being evil themselves. Evil clerics of some faiths walk openly (and are often at least tolerated as long as they obey the local laws). There is still good and evil, don't doubt that, but it's not as black and white as many think.
6. Realms-specific magic. There are a few specific things about magic in the Realms, which are generally covered in the FRCS but you should be aware of. First is Spellfire, there are rules for it int he FRCS, but it's almost best as a plot device (the ability to absorb magical energy and throw it as raw power, it's like having a super-powered version of a Sorcerer's innate magic). Mage Runes (every Sorcerer or Wizard can adopt a unique symbol as their signature) and Mystra ensures that no two mages choose the same symbol, and the Trifold Curse of Mystra (if anybody attempts to forge anothers Mage Rune for purposes of deception, they are struck by a powerful divine curse). Don't forget Mage Fairs (semi-secretive annual conventions of arcane spellcasters, where mages meet to deal in magic items and new spells, talk shop, fight normally-nonlethal duels, play magical games, and take on apprentices.) There are also Dead Magic and Wild Magic zones, rare places where the weave of magic that permeates the world has been damaged or destroyed by a great cataclysm. Lastly, there is the Shadow Weave, mages who have sold their souls to Shar, goddess of Darkness, to access a strange kind of shadow-tainted magic, it's weaker for evocation and transmutation but stronger for illusion and enchantment, and it is immune to Dispel/Antimagic effects unless they are from another Shadow Weave user.
For a desert/waste region and a dangerous frontier town near that wasteland, I'd suggest the Silver Marches region, a loose confederation of small towns in the northern reaches of Faerun (the terrain is fairly reminiscent of the Pacific Northwest) with a relatively small city of Silverymoon as the capitol, and use Anauroch as your desert wasteland (which borders the Silver Marches). The Silver Marches region book was one of the first 3e Realms books, and while it's 3.0 and probably OOP, it shouldn't be too hard to find. The Silver Marches are probably one of the most popular places to begin a campaign (along with the Dalelands).
As for other books, of current materials I'll say that the Players Guide to Faerun was pretty good, if you already have the FRCS, the PGtF is definitely the second thing to get (then Silver Marches if you're running there), that should be all you really need.