Warcraft is much more processor dependent then video dependent.
But that doesn't mean the video cannot be the bottleneck in the system.

I'd start with this list:
a) If you lack sufficient ram (1GB for the OS, plus 1GB per client), that's the largest performance hit and the cheapest upgrade.
b) If you don't have a 64-bit Operating System, you cannot use more then 4GB of ram (including system + video).
c) A low-end SSD, purely to host your gaming folder, 30GB is large enough... don't put your operating system on a crappy drive, but purely for read actions this will rock.
d) A stronger processor, generally you want a Quad Core, the newer i7's are very nice too, but hardly necessary.

You can also change your wow settings.
Disabling shadows is a huge impact.
Weather effects, spell effects etc are smaller impacts.
View distance reduction can help a ton, but I like to keep this to at least half.
Ensure your anti-alaising is set to 1x, 24-bit, and not 2x or 4x.
Disable V-Sync can sometimes help, as that forces your FPS to a 60 FPS (or halves/doubles starting at 60).