Your initial consultation with an attorney should provide you the information you need to take the next steps. However, it rarely hurts to be prepared.
Regardless of where you are in the process, there is almost always the opportunity to gather new information. However, it is usually better to start as early as possible investigating the following items.
Burden of proof
As explained on FindLaw, personal injury cases seek to prove that someone else is responsible for your injuries. The extent to which they are responsible and negligent would typically determine the amount of money they owe you, along with the total amount of your loss.
Factual evidence is typically the cornerstone of any given personal injury case. Sometimes, that evidence has a practical expiration date: A period of time after which it becomes impractical or even impossible to collect.
Certain articles may start to become less detailed and relevant from the very moment your injury occurs. Examples include the physical appearance of the victim, the mental state of the victim, loved ones and family, the conditions at the time of the accident and the impressions left on witnesses.
In general, it is wise to collect as much information as possible regarding these and any other potentially relevant pieces of evidence. While you could always determine later that the record was not useful to your argument, it is difficult to re-create situations and refresh witness memories days or weeks after the fact.
Some of the evidence of your case is probably not available at the early stages. You or your loved one might be waiting for medical imaging results to determine certain complications of your injury, for example.
To summarize, although you should probably collect as much information as possible as early as possible, some vital elements of your argument may take some time to present themselves. As a result, you may not know immediately how much compensation you deserve — and you should therefore probably review initial insurance offers with significant skepticism.