I'm late to this topic but it's an interesting one. There's been some good advice given and some that should be adjusted some. My experience and training has been in CA as a cop for almost 25 years so things may be a little different in your individual states, both in the laws and in how cops are trained. I spent over 16 years in Patrol and 8 years in a DA's Office on the prosecution end of things so have seen quite a bit of how both police and attorneys look at these types of cases.
In general, Oldtimr was right in that you shouldn't shoot in self defense unless you or another person is in imminent danger of death or serious bodily harm. His example of a guy with a knife 50 yards away is a good one. Yes, the guy with the knife can obviously be dangerous but he's going to have to run over to you or at least be within reasonable knife throwing range before he's an imminent threat. The imminent threat is basically a scenario or situation in which you have no choice other than shoot or get killed or seriously injured.
Super Hunt has a lot of stuff right like shooting for center mass (biggest part of the body and easiest to hit). When you're in a shooting situation, you are going to be in a fight or flight state of mind or just freeze and shut down. Training at the range helps you prepare for thinking through such a situation. In the fight or flight situations, you have a good chance of having tunnel vision and losing some of your fine motor skills. Training to shoot center of mass helps you to work through both of these possible phenomenons.
I disagree with Super Hunt about stating you were shooting to kill. Police are trained to say they were shooting to stop the threat. You aim at the same place (center mass) and obviously shoot until the threat is stopped (more than one shot might be needed to stop the bad guy) but your goal was to defend yourself and stop the threat to where you're safe from further attack.
If you tell the police that you were shooting to kill, they are obviously going to write that in their report. The DA is going to look at that statement and so is the defense attorney and any civil attorneys if there's a civil suit. Police are trained not to say they were shooting to kill so some attorney doesn't try to ask you silly questions about being a judge and executioner, etc. in front of a jury, criminal or civil. Hey, there's something like 600,000 cops in this country and if they learn to say shoot to stop the threat (instead of shoot to kill), don't you think it might be wise to use their same verbiage which was developed out of police shootings and lawsuits? You're going to shoot at the same aiming point and you're not going to stop until the bad guy stops attacking you BUT you stop shooting once the bad guy isn't attacking you any more because your need for self defense stopped when his attack stopped and you were safe.
I like what Massad Ayoob has to say and agree with just about all of it. I disagree slightly with him as to the first person to call 911 being listed as the victim in a police report. Yes, they will be listed as the Reporting Party in the CAD (Computer Aided Dispatch) report but the police officer is going to investigate when he arrives and he/she will determine who to list as victim and as suspect in their report AFTER they have investigated.
You or the suspect may call 911 but it might also be a witness or some bystander who doesn't know anything about what happened or just saw the last 5 seconds of the situation before calling. Regardless of who calls, the police are not going to get all the relevant details over the phone and are going to need more information to figure it out.
Massad makes a good point in holstering your weapon once it's safe and keeping your hands up and away from the weapon (makes the officer's comfort factor go up). He also makes an excellent point in telling the arriving officers who the bad guy is, who shot, etc. He rightly points out that you need to know what evidence there is to collect it. It also helps to know what happened so you can figure out how wide to make the crime scene that you're taping off so evidence isn't destroyed. If the cops know the bad guy fired a gun at you, they're gonna be looking for it and the detectives will want to swab the bad guy's hands for gunshot residue, etc.
There's always a balancing act of how much information to say and what not to say, whether you're a citizen who shot someone or a cop. You do want to get the public safety information out right away, like there's an escaped suspect with a gun, the bad guy threw a gun over by that playground, etc. for obvious reasons. And of course that you were attacked and had to defend yourself from the bad guy.
I can't speak for the cops in each of your states and there's always a few bad apples in any business BUT most cops really do want to catch the bad guy and they really don't want some scumbag criminal make them look stupid or get away with a crime (makes it kind of personal). Even just a minimal statement can point us in the right direction and make sure the scumbag criminal doesn't "point" the investigation in the wrong direction (at you). YMMV in your state of course.