For corners, edges and the top, you're looking for as much physical uniformity as you can get. Consider corners and ends the most important "tie" stones, as they're the most exposed and bring the whole thing together. They should sit perpendicular to the wall itself, like the other tie stones, while also working as mini-faces in their own right, holding the smaller interior bits inside while they settle. (A mortared wall especially counts on corner/end ties this way, since the entire structure is being held together by ingredients beyond gravity.)
The top stones are called "capstones" and generally should be as long, flat and uniform as you can find and hold back during your building process, to a reasonable weight. You don't want to injure yourself, of course, but you also don't want to create uneven weight stresses at the top of your wall. On the other hand, since you don't have to worry about holding up subsequent courses, you also get to have some fun with this level.
In closing, it's important also to note that -- as with any DIY project -- upkeep is a factor. While you're designing and working for permanence, and doing your best to build something that will last forever, you should keep an eye out for changes over time. Gravity works more slowly than we can see, which means issues may take a while to show up.
But the great thing about building something like this, with your own hands, is that repairs are made so much simpler. If a part of your wall develops issues, you already know how to fix them -- and you've already practiced for just such an occasion. After all, the way you've chosen to build your wall makes it a snap anyway. A mortared wall with cracks just needs mortar, and a dry-stone wall? Simple as stacking one stone on top of another.