I would use 1x6 rough cut poplar or oak for the rails, that's what I build my horse fence with, and they hold up okay as long as you paint the fence after the lumber is well dried. Cost around here is .40 a board foot for poplar, little more for oak so it is fairly economical. Also - I would price 4-5" round posts versus the 4x4 squares, the rounds are more irregular, but also it's more wood in the ground. Where I am in Alabama, a 1/2 bag of quickqrete is no better than filling the holes with gravel or dirt. So I either put in more concrete, or just skip it. If you do concrete, put in extra at all of the corners, and if you have the energy the posts next to the corners as well. Your corners, and the first & last posts when you stretch your fence are the ones more likely to move. I would over due anchoring posts, lining them up, etc before stretching the wire. Nothing is more frustrating than a poor fence - I've installed way to many feet of bad fence that I've had to replace in short order. Also - I've had terrible luck with the welded wire that sells for .50 a foot at the big box or TSC. I've been happier with the woven field fence that is actually cheaper. It's a bigger grid though, so not sure if it would work as well for dog fencing.