A 150 linear foot fence line is the typical size for enclosing an average suburban backyard. At a 6-foot height with 8-foot on-center post spacing, this requires 20 structural posts set in 40 bags of fast-setting concrete, 57 2x4 horizontal stringers, and approximately 330 dog-ear pickets.
With 8-foot post spacing and one 4-foot walk gate, you need 20 posts (19 sections + 1 gate latch post). At 2 bags of 50lb fast-setting concrete per post hole, order 40 bags of concrete.
Always use 3 rails for a 6ft privacy fence. A 2-rail fence will allow 6ft pickets to twist, bow, and cup under summer heat and winter moisture within 18 months.
Post holes should be dug to at least 24 inches for a 6-foot fence, or below the local frost line (up to 36-42 inches in northern climates) to prevent winter frost heaving.