If you are shooting for realism, the best eyes textures should not contain any burnt in reflected images or specular reflections.  All the adjustments are performed in the material room with the right type of shader nodes to enhance the image.  Then it comes down to the environment your character is set up in.  A self illuminating skydome or an enclosed room adds more credibility to the way eye textures respond to existing light.

The best set I have come across, Elite Eyelights @ DAZ3D.  You can build up the different eye layers with more realistic results.  And I never need to post work.