After my old fence blew down in Hurricane Irene, I shopped around and selected Hercules Fence to replace it. They’re a DC-NOVA-MD-area firm. http://www.herculesfence.com/
They hauled away the old fence and build a new, 7 ‘ 9″ fence out of pressure treated wood, with black-capped posts in a concrete base, and a rear cedar gate. My new fence looks similar to the one in the picture you posted in your question.
I was very satisfied with them. It took them about two days from start to finish, including stopping for a rain delay at one point. I paid about $3,350 for the 110′ length of fence they built, including the cost of the haul away of the old fence.
I shopped around and Hercules was the best value I could find, in terms of both price and quality; but whether you use them or someone else, make sure the price you pay includes haul away of your old fence.