Final Fantasy XIV Minimum System Requirements

FFXIV Operating System
Windows XP SP3*
Windows Vista 32-bit/64-bit SP2**
Windows 7 32-bit/64-bit**

FFXIV Processor
Intel Core 2 Duo (2.0 GHz)
AMD Athlon X2 (2 GHz)

FFXIV Memory
Win XP: 1.5GB
Win Vista/7: 2GB

FFXIV Storage
Install: 15GB
Download: 6GB

FFXIV Video Card
Nvidia Geforce 9600 series with 512 MB VRAM or equivalent
ATI Radeon HD 2900 series with 512 MB VRAM or equivalent

FFXIV Sound
DirectSound compatible sound card (DX9.0c)

FFXIV Internet requirements
Broadband Internet Connection

FFXIV Resolution
1280 x 720 320-bit

FFXIV DirectX
DX 9.0c

FFXIV Controls
Mouse, Keyboard

* If using Windows XP, the excecutable files, installation and version updates should be set to Administrator settings.
** 64-bit operating systems will run in WoW64 (Windows on Windows 64) mode.

There is a benchmark tool on the official website.
2500 seems to be the lowest score that would comfortably run the game on default settings. All of the possible results are listed below.

[8000 and over] Extremely High Performance
Easily capable of running the game on the highest settings.
[5500-7999] Very High Performance
Easily capable of running the game. Should perform exceptionally well, even at higher resolutions.
[4500-5499] High Performance
Easily capable of running the game. Should perform well, even at higher resolutions.
[3000-4499] Fairly High Performance
Capable of running the game on default settings. Consider switching to a higher resolution depending on performance.
[2500-2999] Standard Performance
Capable of running the game on default settings.
[2000-2499] Slightly Low Performance
Capable of running the game, but may experience some slowdown. Adjust settings to improve performance.
[1500-1999] Low Performance
Capable of running the game, but will experience considerable slowdown. Adjusting settings is unlikely to improve performance.
[Under 1500] Insufficient Performance
Does not meet specifications for running the game.

There is a Japanese website with hundreds of different benchmark scores for your reference.