What information should be collected and analyzed that would be most helpful in developing laws to protect and/or regulate the right to bear arms...

If I understand your question correctly, you are asking what data could be used to strengthen the Second Amendment and what data could be used to weaken it. Any laws, regulations, or ordinances would flow from one of those stances, assuming you would be arguing to Congress, to a state legislature, or a municipal governing body to enact any kind of legislation consistent with the amendment.  In the first instance, it would make sense to...

If I understand your question correctly, you are asking what data could be used to strengthen the Second Amendment and what data could be used to weaken it. Any laws, regulations, or ordinances would flow from one of those stances, assuming you would be arguing to Congress, to a state legislature, or a municipal governing body to enact any kind of legislation consistent with the amendment.  In the first instance, it would make sense to find data from nations that have weak or no gun control laws and yet have a very low rate of murder, suicide, and injury with guns. Similarly, if there are states or cities in the United States with weak gun control, and they have low rates of gun violence, death, and injury, this would bolster an argument that the Second Amendment should be read as broadly as possible to protect the rights of individuals. On the other hand, if you are seeking to make an argument that the Second Amendment should have limitations, i.e., you are arguing for stricter gun control, you are going to be looking for statistics from places that have strict gun control and have a lower incidence of death and injury from guns, which is going to make your case for you.  If you find places that have no gun control or weak gun control and very high rates of death and injury as the result of guns, that will make your case for you, too.  While I have by no means looked at statistics like this from everywhere in the country or everywhere in the world, I strongly doubt that you will find much in the way of support for the contention that society is safer and happier with no gun control or with very diluted gun control.