Chris, the most important thing is to be sure you are inside your lot line and talk to you neighbors, just to let them know what's going on and try to work out any complains.
The general rule for fence posts is 2/3's above ground and 1/3 under ground. Since you probably will have to buy an 8' post, you can easily go under the frost line. Don't forget to measure to the bottom of the post, not the bottom of the hole, since a couple of inches of gravel or crushed stone will let the post last a lot longer. And pressure treated will outlast anything else in the ground but you have a wider choice of woods above.
My feeling is that the gate posts should be in concrete and either is OK for the intermediate posts. With the new concrete products where you just pour a couple of bags in the hole and add water, you might find that this is so easy, you may not want to mess with pounding down dirt. This is hard work on a hot day. If you do use concrete, be sure to crown the top of the concrete so water will run off, even if the top of the concrete is a couple of inches under the soil level. Henry in MI