Don't give them anything to use against you. you don't have to tell the entire story, but withholding info and acting like a belligerent punk is a GREAT way to turn sympathetic officers into adversaries.
You assume that they are sympathetic to your case, and you're probably right in most circumstances. However, CCW is very unpopular in major cities and especially in blue states, and the political (read liberal) climate isn't necessarily in the favor of the SD shooter. If you don't believe me, check out Huff Post when some gun related topic comes up. I would describe those people as rabid haters, and they vote, too. There are DA's out there that look at prosecuting a SD shooting into a murder conviction as THE political stepping stone for their careers.
Research the Harold Fish case that Atomic Punk posted. I would have thought Arizona was very gun friendly, but this DA had to convene 4, repeat, FOUR grand juries to get an indictment, because the first 3 no-billed it. Then, the judge suppressed most of Fish's defense, including multiple incidents where the deceased made violent raging assaults on people over his dogs. The judge also did not properly instruct the jury, and did not follow AZ law which removed the affirmative defense mandate for self defense. As a result, Harold Fish spent 3 years in prison for murder 2. An appellate court finally granted a retrial, which never happened because the first trial was a railroading miscarriage of justice. BTW, several jurors that convicted Fish mentioned in interviews that the case the DA made about the 10mm Fish used to shoot the nut case assaulting him played into their decision to convict him of murder.
Maybe the Fish case is the exception to the rule, but I'll take every advantage I can to not spend years of my life in prison. You don't have to be a belligerent punk to not answer irrelevant questions that are aimed at building a case against you. It can be done in a very professional manner as your 5th amendment rights, and if the cops are truly sympathetic to your case, they will understand why you don't want to answer certain questions. And if not, then they're probably trying to screw you.