can a pci express x16 motherboard work with a pci 2.0 x16 graphics card?

I have a pci express x16 motherboard and I want a new graphics card with pci express 2.0 x16 but I’m not sure if if will work. Also, what the best for the price- Nvidia 9600, 9800, or ATI 3870? http://bit.ly/kr0A3O