I'm currently fencing in about 25 acres for my horses and goats. I'm using 2x4 horse fence that's 48 inches tall. My round wood posts are 100 feet apart or less, and my T posts are every ten feet or less.
When I do the front of my place, along the paved road, I'm going to make it nicer looking with 4x6 wood posts every 8 feet. I will use a 12 inch auger every 8 feet and try to get 3 feet down. Sometimes I just cant get that far, but I do everything that I can to try to get that deep.
Every post will be filled with concrete. I built up the concrete so it's above the surrounding ground, and causes the water to flow away from the post. As a contractor, I've replaced quite a few fence posts for clients, and in every case, they rot right at ground level. Some are in concrete, a lot where just set in compacted dirt. The dirt is the worse because it settles, or washes away over time, and you end up with a small pond around the base of the post. Water sits there when it rains, and this is what rots out posts. If water cannot sit next to the base of a post, the post does not rot.
Early on, I set some posts in concrete, some in dirt. I've pulled both of those posts with my tractors, and the ones in dirt come out just as easy as a T post. I can pull them out with my smallest tractor just idling. The posts set in concrete are night and day harder to get out. I can only get them out with my full sized backhoe, and the engine has to be revved up to have enough power to get them out!!!! More money, more work, but much, much stronger post that will last a lot longer.
A 12 inch auger isn't really big enough to line up a bunch of posts. Even without trees close by, you never know what you will hit in the ground, or if the auger will just start to angle on you while going down. What might seem like a small variation when drilling the holes will become a huge issue when setting the posts. Buy the biggest, heaviest, strongest clamshell post hole digger that you can find. You will be modifying your posts after drilling the holes if you want to get the fence in a straight line.
I use 4 pt, high tensile barbed wire for my string line. I tried using string, then heavy duty string, and even a small type of rope to pull a straight line. It just doesn't work very well over any sort of distance. Either it breaks, or it doesn't ever get straight. You really notice this when putting posts in and moving it out of the way to get the post in the ground, the putting it back to line everything up, and it's caught on something, or its stretched out and needs tightening again. Barbed wire will stretch a little when doing this, but nothing close to string. I also like having it under my fence to discourage coyotes and hogs from digging under my fence.
In my opinion 1x6 boards are too flimsy and will sag over time. For the most strength, you want your boards to attach to at least 3 posts, so 2x6x16 are the best option. I personally only use screws for every exterior, outdoor project. Nails always pull out over time. For fencing, I like 4 inch deck screws.
I agree with the earlier post that 4 rails is better then 3. When I build my front fence, it will have four rails.
Round posts are cheaper, and they usually have better treatment then 4x6 or 6x6 posts, but they are a lot more work to attach wood rails to, and in my opinion, they don't look as nice as square posts. I also like having 5 1/2 inches to attach each rail to the post.
Are you running any electric? The goats I had must have been descendants of Houdini, they could figure a way to get out of anything I put them in.