overweighted Automatic Rigging Issues

One thing you can consider doing is using helper bones. These are deforming bones that exist only to get better weights from autoweights-- after you have good weights, you can delete the bones and drop the weights to their parents, or just leave them around on some junk bone layer where the animator won't ever be bothered by them.

The selected bone, parented to the root, will suck up some of the autoweight that would otherwise go to the "arm" bone, so the armpit won't deform as much as the arm bends.

Sometimes bones influence the wrong areas of the mesh, like the arm influences the torso in your picture. Automatic weighting is fast, but sometimes not very smart. One thing you can do to help make it smarter, is to use the buttons in the Weight Tools Panel, directly after using automatic weights. In the case of your example, maybe try using "Quantize" or "Clean", with the subset set to "All Deform Pose Bones", and "Steps" set to 4. You can experiment with the number of steps, and the subset, as well as the buttons in the Weight Tools category.

1. Select mesh
2. Select armature
3. Ctrl + P > "Automatic Weights"
4. Select Mesh, go to "Weight Paint Mode"
5. Go to the "Tools" tab choose "Quantize" or "Clean"
6. Press "F6" ; Subset = "All Deform Pose Bones" ; "Steps" = 4

Well, that's a normal behaviour. You can either add a bone to control the Neck part as WhovianBron3 suggested, or you manually fix it. The reason this happens is because the bone has high effect on this part of mesh because it is close enough to it.