Fences are pretty easy to install. Why not build it yourself? Use the wood screws made for pressure treated wood, not nails. For my fence, I rented a tow behind auger from Sunbelt which was very easy for one person (me) to drill the necessary post holes. Skip the cheap two person handheld because if you hit a rock with that thing, you're gonna be hurtin'. Get the little plastic tumbler concrete mixer and use Quickrete, works very well.

For 6' it's called a "privacy fence" so you may want to check if there are any homeowner association restrictions first if applicable. Do you have accurate survey lines? Got mine with the mortgage closing documents and there were metal spikes underground to mark the property lines. Found those pretty easily and used string to mark the property lines before building. Had to keep the fence something like 6" on my side and not directly on the property line, iirc.