I am not sure where I am on the sexual crimes debate, I think Police definitely need to make sure they balance out the prospect of there being more victims (and so contact the media) with the likelyhood of the suspect having a fair trial or a life after a false accusation.
In terms of other crimes though, I think far too much information is given to the media by various sources and far too much is disclosed by the Police to them.
If something like a murder happens and the Police catch or name the suspect then they should be named and that is it. I don't think thhe Police or Media should describe the gory details of the crime until the crime is in court and can be reported on.
There have been many, many cases throughout history in the UK and the USA where by the time a case has come to court there has been so much media attention about the suspect is near impossible to get a fair trial. So much so that when selecting jurors they have trouble finding any that don't already think the suspect is guilty, before the trial has started!
So yes for serious crimes the Police should say what the charge is and who they have arrested / are looking for. That is it, nothing given to the media and they have to wait until details are given to the court.
This would hopefully mean jurors can make a balanced decision on just the evidence, rather than being pre-influenced by all the interviews and articles in the media that will see over and over again before a trial.