Julie, there are a lot of reasons why wood moves. Humidity and the moisture content of the wood is one of them but things like mechanical stress from growing conditions being released and improper sawing techniques at the mill are others. The good news for you, though, is that you should be using pressure treated (PT)wood and, since the better PT wood is warranteed, it is handled pretty well. You are correct that wood movement is apparently less in thicker wood and with PT wood, the treating process relieves a lot of the stress. You want the highest retension rate that you can get for the posts in the ground and 40% for the wood that's above ground. 60% retension is available but you may have to settle for 40% for in ground use. Much of the PT wood is "treated to rejection" and, since no one knows what the amount of chemical involved is, I would not buy that for a critical project that you want to last.
You may be concerned about what you have heard about the safety of PT wood, but if you will look at the facts, you will see that it really is pretty safe. I do not think that I would like to see a kid licking it like an ice cream cone, but you can say that about a lot of things that you can find outside. The EPA studies it extensively and finally bowed to pressure from environmentalists to mandate some changes. This means that the PT wood manufacturers will drain and clean their tanks and refill them with chemicals that do not have the history that our current PT wood has, but the warrantees will still be as long. In any case, there is an element of danger from using wood that will not protect itself from insect and water damage as this can be eaten from the inside until it falls down.
Since you will be using PT wood, you will want to wait for a few months before you paint it, in any case. Painting it, after an accommodation period, will make it more decorative. The green look of PT wood will bleach off the surface during this time. There is no doubt that oil based primers are better for outside wood. Their chemistry adapts better for allowing the movement to occur without separating the wood and primer or the primer and paint. Water based paint is getting better in this regard, and it is close to a toss-up now.
Your best bet in choosing a paint is to follow the same practice that you do when choosing a contractor. Your local guy that has been in business in your area for a long time knows your local conditions better than anyone on the web! The paint and the paint store that he uses will be the best around for the projects that he wants to last. He stakes his reputation on it. It's the same for the local paint store. Every satisfied customer is good word-of-mouth advertising. Every dissatisfied customer will tell 5-10 people what a rotten experience they had. The stores that give consistantly bad problems and advise don't last. Carrying this farther, paint brands are the same. Tried and true brands like Sherwin-Williams, Benj. Moore and some others, are the way to go.
My feeling is that, if you want good paint in your local area, you go to a paint retailer who handles a top line paint. You ask them what they suggest and you follow their direstions to the letter. A home center sells paint--and lumber--and tools and on and on. The paint store you want to use may sell wallpaper but that's about the extent of the best ones. They have to know what they are doing to stay in business in your area. It might cost you a dollar or two more than what the big box stores will charge, but the local operation will more likely take time and answer questions. They want you to succeed and their success depends on it.