Our role as a Dungeon Master, beyond being a rules lawyer, storyteller, and narrator is to take each game to that next level.
To suspend space and time for a few hours, immerse out players in a fantasy world, and allow them to BE the characters that they are playing.
Suspense and changing of belief. Certainly Dungeons & Dragons is a game of the mind, and one can play fully old school- just some graph paper, dice, and a character sheet. But there are other arcane and esoteric tools at the command of the Dungeon Master. Miniatures. Using miniatures in your game is a way to not only add new depth to the game, but also a way to manage encounters better. Placed in the center of the gaming table, miniatures become a focal point for your players, and an anchor point during encounters.
They represent the adventures, monsters, and perhaps even the furnishings of the dungeon itself. Distance, range, and what can an can't be his is all laid out- it makes the game more tactical and precise, and allows each player to physically interact with the miniature as an avatar on the table. So where to start? You don't need miniatures for every game.
Build your collection slowly over time. Start with the low level monsters- stuff you will always be using, and over time add the icons of Dungeons & Dragons to your collection- dragons, beholders, vampires, liches, etc.