If you just want to pose the arm, use the Manipulate Bones tool. By default, this tool animates a bone chain using IK, so there is no need for a Bone target. Bonus tip: when you press and hold Alt, the Manipulate Bones tool switches to FK mode so you can pose the individual arm segments. For example...
A Target bone is best used for pinning the arm/hand to something, like a tabletop or the hips of the character. For example...
In the above example, I'm first using Manipulate Bones without Target bones to animate the arms freely. Then, I'm targeting the forearm bones--one to the Table Target bone, and the other to the Hip Target bone. Then I'm using Manipulate Bones to move the Torso Bones.
Sorry, these examples are a little sloppy, but they should illustrate the techniques accurately.
As for why the target in your example is acting spazzy: test it on a non-zero frame. Frame 0 is the Setup frame, and rig testing should always be done on an Animation frame. You can get away with testing a few basic things in frame 0, but not everything works there the way it works on an actual animation frame. You can use Toggle Frame Zero to jump back and forth. (Setting this to a shortcut is wise.)
Hope this helps.
Note: the blue guy example was tested on frame 0. I can tell because I see the Bone Strength capsules. In this case, I got away with it because this is pretty basic. To test anything more complex, I would have had to step into frame 1 or later.
