I am going to buy a lens hood for my AF-S DX NIKKOR 18-55mm f/3.5-5.6G VR. I searched and I found out that the best lens hood is Nikon's HB-45 lens hood. However, I also found a newer version, the HB-45 II lens hood on Amazon Is it compatible with my lens? I prefer the petal shape of the II version.
I own an HB-45 lens hood, and it works very well. I prefer not to use UV filters, as I don't like to cover my lens with lower-grade glass, so lens hoods are generally my only protection.
It may not look as good as petal lens hoods, but in this situation with this lens, a bayonet lens hood works perfectly. I have never experienced any vignetting, and it's easy to apply and remove. That being said, as AJ stated, the petal lens hood that you linked to is a third-party hood and likely not as quality as the HB-45. Additionally, the way that the lens ring rotates -- as Szabolcs pointed out -- would cause the petal hood to rotate, removing any value as a device that blocks oblique light rays coming in from the side. I would stay with the bayonet lens hood, as that's your safest bet, and really doesn't look too bad.
Nikon does not appear to make an HB-45 II lens hood. If you look at the images, it appears that they are attempting to sell a third party product under the guise of being an upgraded official product. If you look at Nikon's product page, the HB-45 from Nikon is the officially supported lens hood that is designed to be used with your lens.
As szabolcs pointed out in the comments, the lens petal hood won't even work properly since the front of the lens itself rotates which would move it out of position and would result in inconsistent results that would cause a deterioration in image quality. Personally, I'd rather trust the style that the manufacturer (who knows the optics) built to work properly with it. The third party one may or may not be particularly effective or well built. I'd be particularly concerned by the fact they were trying to make people think their product was a newer Nikon product. If they are dishonest there, where else might they be dishonest?