this is also a pressing question to me months ago for the Note2 and Note 3. I preferably like White Devices, but for the Note 2 and Note 3 / Neo, I would skip white and go for the black. The White one has a diamond-shaped pattern that would probably be popular with the ladies whilst the Black one has the more-masculine and classier brushed-aluminum look.
here's a photo to compare both:
Regarding the back, I believe it's more of a personal preference. I like white on my devices, but for a more "leather-y" feel, black definitely.
Green, lol! No, just no.