What kind of wood? Treated or untreated? Clear or construction grade?
In lumber, the word "clear" means "without knots." How important this is varies depending on your project and whether you are free to sift through the pile of lumber at the lumber yard looking for the best piece. If you are applying plaques to the pole, knots are okay.
If you are carving your peace pole, you must get wood that is clear, at least in the section to be carved. If you are painting it, a few knots might not be a problem, depending on where they are and how big they are. Knots are the first thing to deteriorate as the pole weathers. Knots expand and contract differently than the surrounding wood and can fall out leaving a hole. If that knot is in the middle of the "a" in peace, it might not be the effect you want.
Cedar is a common choice for peace poles because it resists rot and bugs so well. But you have to be careful of clerks in home improvement stores who sometimes casually refer to their wood as cedar when it only is pine. Real cedar is more expensive. Especially if it is smooth cut and clear.
Most people in construction want cedar that is rough and full of knots because that is the look they are seeking and so that is what lumbar yards mostly stock. It can take some searching to find smooth, clear cedar.
Depending on your project you might not need smooth cut. Getting it smooth cut can cost 4 or 5 times more because of the nature of cedar. Cedar trees have lots of small branches growing from every area of the trunk, which is why they make good Christmas trees. So cedar naturally has lots of knots.
However, at the time of this writing, a rough cut 6 by 6 that is 10 feet long, which is the size I recommend for peace poles, is $60 most places. If you are painting the text on your peace pole, find someone with a belt sander, or rent one for $5 a day from a tool rental, and belt sand just the area where the text will be. That will make a nice frame for your text.
If you are painting the entire pole, standard untreated construction lumber might be a good enough option in some circumstances. It is inexpensive (perhaps $6 for a 4 by 4 post 8 feet long or $30 for a 6 by 6 post 10 feet long) and will last as long as your paint. Why pay for a post that lasts longer than the paint? To keep untreated wood from rotting as a result of being in contact with the ground, look at these installation options for ways to handle that.
I recommend getting a 6 by 6 post 10 feet long and burying 2 feet of it. Peace poles should have stature equal to the message. It takes a certain amount of size to achieve that.
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By the way, what is smoother and clearer than cedar, usually less expensive, can last even longer and is more environmentally friendly than cedar? Redwood, a wood that is politically incorrect and could result in my being harassed for mentioning it. Cedar is cut from virgin forests in Canada. Redwood comes from a tree farm in California that is the size of the state of Ohio. That farm was planted in order to raise redwood as a crop to be sold as lumber and then replanted - a sustainable forest. But redwood is a hot button that causes politically correct hackers to damage your website and send nasty emails. So everyone uses cedar.
However, at least one do-it-yourselfer has made her peace pole out of Redwood and lived to tell about it: http://wolfftracks.blogspot.com/2009/06/peace-pole-dahlonega.html. She's a retired art teach with a very deft hand at painting letters.