- A woven construction with an s knot, which I had decided I wanted instead of the welded wire for strength and has the added bonus of not catching on my dogs' or future goats' fur
 
- 2x4 openings, so no stuck heads or hooves
 
- 5ft tall(!) to stop my dogs from jumping and a 200ft roll 
 
- 4x4 posts every 8ft set 2ft in ground with cement. (6 ft posts where gates are added)
 
- Bottom rail will be to the ground. Top rail will be at 5ft.
 
		 
		
	 
I slimmed down your post to just the points I want to address.
I think you will be MUCH happier with the woven wire vs. the welded wire. Woven wire is far superior, both in gauge, tensile strength and ability to withstand abuse by livestock and pets.
On the posts.... you should also price out round posts - 4-6" rounds for line posts (or even 6" half-rounds!). These are often cheaper than 4x4 posts, and IMO, for whatever reason, they last longer then the 4x4's. I do not know what to attribute it to, maybe it is the fact that the rounds "keep" their "trunk" shape??? Any professional installer can just as easily use rounds for the fence you describe as using 4x4. Just make sure you DO NOT let ANYONE convince you to use landscape timbers as line posts.
You may want to reconsider the concrete for your line posts. While concrete *seems* like a good idea, the first time you have to replace a broken line post, you will be cursing your decision as you have to dig up the concrete to set the new post. There is also some speculation out there that the concrete "holds" the water around the posts, causing them to rot off faster.
In order to tighten your fence AND support 10' gates without them sagging, you will NEED to have H-braces made of 
6-8" rounds at your corners, ends, gate hangers, and possible spaced along your lines, depending on how long the span is. H-braces literally make or break your fence. Without them, when you try to tension your woven wire, your end posts will simply lean in, even with wood posts along the line. Your gates will sag, making them look unsightly and likely impossible to freely swing open/close. And even with the gates hung on a H-brace, NEVER EVER let a gate "swing" open in the wind. It is either locked open or locked closed. Constantly swinging gates (like in the wind) damages the hinges and pins. Also consider installing a "rest" for it to sit on when it is closed, thereby supporting it and preventing it from sagging.
Running a bottom rail flush to the ground sounds easy enough, but it really is a huge challenge given the miniscule differences in terrain between each post. You might want to consider running it 2-3" above the ground, instead. Otherwise, your labor costs will likely increase as the installer will have to spend time clearing a "path" for it to sit in. Also, even though the rails will be pressure treated, any contact with the ground will cause them to rot off faster. It is amazing how fast a 1" board can rot away when it is on the bottom. If you don't plan to run any large livestock - like cattle or horses - you can likely just use "deck boards" for your fencing. They are not true 1" boards, but are easily found in 16' pressure treated length. I would NOT recommend using them if you do plan to run horses or cattle, as they splinter and break far too easily. I have spent the last 6 years slowly replacing the deck boards and woven wire fencing that was installed at the barn I manage. One butt-rub from an 800lb pony is all it takes to bust them.