I think it really depends on WHAT story you are talking about.
Any individual event, the FIRST time we hear about it will be a preliminary news report, that will be usually a little sketchy as information is coming in. I would probably trust the basics of that unless something about struck me as being suspicious.
A Malaysian plane went missing, Someone shot people in a school, there was a bomb at the Boston Marathon, a plane hit the WTC, followed by a second one that immediately changed how the event was perceived. Those kind of things.
I would tend to trust the basics of what is reported with more details to be filled in later. There isn't usually an "official story" until much later, although there are certainly some people who would immediately think " I bet that is a false flag operation so Obama can take our guns away" and immediately start looking for holes in the "official Story" that is nothing more than preliminary reports that are subject to change as more data is available.
While it may be true that governments use the media to spread the story they want, I do not believe they are in bed to the point that a completely false prepared original report is made.
I know some CTers will say the Main Stream Media IS the govt, thus making the first reports "official" but I don;t agree with that and so that is why I too feel the question is loaded.
If I stick to the first reports, the BASIC facts I trust unless it appears really implausible or unless someone comes up with some really good evidence to suggest otherwise. Once the media moves onto blind speculation,( for example, the Anders Breivik incident being blamed on Muslim terrorists by the New York Times before any real info had come in) this becomes MUCH less trustworthy and I generally ignore it.
The thing about debunking, is that I would pretty much be trusting the basic facts of an incident but then I will see stuff posted all over FB etc saying THE TRUTH about X, and it is usually clearly bunk from the outset.
When you show that this assertion is bunk, a true believer will have to attack you and accuse you of being stupid and a sheep and always trusting the govt or just being a shill etc when all you have actually done is to point out what is WRONG with the assertion. If they were REAL truth seekers, they would take this on board and re-evaluate their position.
Quite often on Metabunk, where someone comes along with a DEBUNK THIS!!! post and claims this site is spreading lies for THEM, debunkers, particularly Mick, will simply ask them to point out what it was they said wrong and why it was wrong. That's usually when they make a flame post and disappear.
I often don't necessarily pay too much attention to a story until all the bunk comes out.
The Sandy Hook shooting was a terrible tragedy for all involved, but it wasn't just not the first shooting of its kind, it was not even the first mass shooting in the USA that year,(13th of 14 according to the Washington Post:
http://www.washingtonpost.com/wp-srv/special/nation/us-mass-shootings-2012/ so without all the bunk surrounding it, I am afraid that I , like many others would have forgotten about it by now.
It is very useful though to try and see the whole picture, and look at everythign from as many sides as you can.
This advert for a newspaper was brilliant at summing up how our preconceived notions about something or someone can effect how we view a situation if we aren't careful: