You would wait for the police to arrive with a gun in your hand? That seems... dangerous. :uhoh:
That is a good point.
If outside, as soon I sight the first police car responding, I would place my firearm at my feet, keep my hands open and visible, and then do what the officer wants. "That man/woman (pointing at suspect) attacked me and caused me to fear for my life." would be, other than identifying myself as the law requires, my only direct communication to the police.
If inside my home, the only variation to the "outside" scenario would be that I would wait until the officer was at my door and, before opening it to him/her, would then place the firearm on the floor and move away from it. Again, keep hands open and visible, obey the officer's commands, and say nothing other than as outlined. If it is at all possible, make sure you have one or more other firearms in a location in your home that the police will not be likely to search. My reasoning is that it is highly probable that the police will not only search your home after a defensive shooting but will seize any and all firearms and ammunition they find. You do not want to be left defenseless.
There were some very good points about dealing with the media. Basically say nothing to them. That is one of the things you are paying an attorney for.
Another good point concerned family and friends of the person against whom you defended yourself. In today's society, you can expect, at the least, a lot of threats and posturing. At the worst, you will see attempts at retaliation.