makehumancommunity.org

I'm new to this stuff so I'm learning.

One thing I found in Blender is an auto-rigging tool that uses a specific type of skeleton which differs from the skeletons you have shown.

I figured being as that is also a popular tool and it already ships now with an import/export option for MakeHuman files (enabled under the user preferences > addons menu) - that matching another add-on's layout might be a good thing to look into - especially as that skeleton model has a pre-set tutorial on how to apply and adjust its rigging.

Just a thought.

MakeHuman can export a rigify compatible rig. Which is to my knowledge Blender's best "auto rigging" tool.
MH's rig names are also compatible with Blender's symmetry system.
Otherwise I don't know what you mean, but surely Blender does not have one single standard rig (that would kind of defeat the purpose of it being a general tool).