Michael, prior to enlisting in the military, you will be given a test to assess your aptitude to succeed in various fields. I do not know how the military scores this for military police.
I worked at the SA Airport PD with many former military police officers. I also had occasion to call out the MPs for misbehaving military personnel. In general, the things that make good police officers, beyond the physical, are the following: decisiveness -ability to make good decisions, quickly. Report writing - ability to identify the key elements of the offense, and make sure they are included in the report - and to tell the story in chronological order. People skills - ability to talk to people, and, get them to talk to you, voluntarily. Legal -ability to learn a complex body of laws, and apply it when faced with various situations. Personal - your personal life is drama-free, to the extent possible. You don't want to be distracted at work worrying about personal problems. This includes having your financial affairs in order . Self confidence - I have seen low ranking military police have to take control of high ranking military officials - you cannot be easily intimidated by them. Leadership - ability to take control of situations.
A lot of this will be taught to you in MP school. If you want to be an MP, I encourage you to discuss this with a recruiter. Take a practice test and see where you stand. If you need help studying to raise your score, get back with me - I have test-taking tips.
Best of luck!