We spent the first weekend cutting the lumber to length and applying two coats of primer to all surfaces. The next weekend, we dug and poured concrete footings and applied two topcoats of paint to the parts. Then we took one more day to build the arbor and paint the posts, which arrived the day before construction began.
The arbor was built entirely of construction-grade redwood, which resists rot and insects. Although cedar and pressure-treated pine are also rot- and insect-resistant, redwood is friendlier to work with. It's lightweight, soft and very easy to cut and shape. It's also less likely than pressure-treated pine to warp or twist, and it holds paint beautifully.
The total cost for the redwood was about $1,500. Western red cedar costs about the same. If you're willing to sacrifice some dimensional stability, use pressure-treated pine, which runs significantly less—just about $600 to $700.