The short answer is that everything has to be documented at a crime scene. The more detailed your notes are, the better your chances of solving the crime later. We cannot leave crime scenes alone forever, and even if we did they would never stay exactly as we found them. Evidence gets moved, stolen, dried up, and so on.
For practical purposes, the most important thing to do is take as many careful pictures and measurements as possible. If it is a death, you need to pay particular attention to where the body is and how it is positioned, because the body will be one of the first things to be moved. Next you’ll want to focus on other biological or delicate material. Look for shoeprints, blood pools, fibers, hairs, and anything else that will not likely stick around long. These things need to be documented as closely as possible.
Fingerprints need to be taken on any important surfaces, and elimination prints of people who had a legitimate reason to be in the room. Fluids can also be checked for with special chemicals and lights.
A murder investigation is extra important. The Medical Examiner will check the body to see what the temperature is. They can determine the time of death this way. Also, the ME will try to determine a preliminary cause of death so that investigators can try to look for a suspect as soon as possible.
Another important thing to document is the murder weapon or instrument of the crime. If the weapon is still at the scene, its position needs to be photographed, measured, and carefully described. Any other evidence such as bullet holes, shells, or scratches need to also be documented carefully. These things could mean a conviction for the culprit later.
All evidence collected needs to maintain a proper chain of evidence. This means that it needs to be bagged, labeled with a time and date and the person who collected it, and passed on with a proper chain of custody. The evidence has to be tracked at every point to prevent tampering.
Forensic science can later determine who the killer or culprit might be, and what happened and how.
The better the information taken at the crime scene, the better the investigation. Not all of it will prove relevant. Crime scenes are definitely a place whre it is better to be safe than sorry.