What is your CPU?
As Eyefinity is extremely GPU-intensive most modern CPU's should have very minimal if any bottlenecking.
For lower-resolutions like 1440x900x3 you could probably get away with a 5850 (overclocking would really help).
For the lower-end dual 5770's or a single 5850 is your best bet.
Higher up dual 5850's will drive even 1920x1200x3 quite nicely (once again overclocking will help).
To clear it up a 5970 is 2 5870's in 1 card, it's the same thing as CrossFire.
For your monitors I suggest using 16:10 monitors (ie 1440x900, 1680x1050, 1920x1200) as 16:9 (1280x720, 1600x900, 1920x1080) look very wide and short.