I'd have to recommend playing the Doom games on PC, actually. I may be perpetuating a never-ending debate by saying so, but in my experience, DOOM controls
far better with a mouse than with a controller, especially considering how fast-paced the gameplay is. Using the mouse to aim is fluid, precise, and is incomparably tactile. On PC, the games' controls quickly become an extension of your thoughts. It's buttery smooth, man!
Of course, if you for some reason are unable to get the games on PC, I understand. In that case, if you're new to the classic DOOM franchise or are aren't well-acquainted with shooters, you may be better starting out with good ol' DOOM 1 for XBLA. As Chary said, playing a game series in order is generally a good idea, particularly in the case of DOOM. While the second game isn't radically different from the first, it often seems catered toward those who've already played through the first game, with levels that are larger and more intricate than its predecessor.
However, if you're confident in your first-person shooter prowess and don't care much for playing franchises in order, getting DOOM 2 might be a good idea. The game is essentially a leaner, meaner DOOM, and the online multiplayer features are considerably more robust.
Regardless of your decision, I think you'll find the game to be more than worthwhile!
(And all things considered, perhaps you're better off not thinking too hard about your choices, like I often do
)