Firstly, the military does things differently, so you should not believe being an MP will give you training for the civilian police force. You will still have to go into the academy and go through all of the training once you go to a local department when you leave the military.
Secondly, never, under any circumstances, join the military to get out of the house. The first reason should be to serve your country, not to use as an escape. It is a life-altering and very serious decision to make and should be respected as such.
Thirdly, don't come here for advice to join the military. True, we do have people from all branches who are members of the community, but the best place to go is to a recruiter. They can answer every question and in more detail as it pertains to you. We don't know what your ASVAB scores are. We do not know your qualifications.
I'll attempt to answer your other questions.
No branch is "easiest". Sure, training in branches vary in intensity, but every single branch is grueling. If you aren't prepared to bleed, sweat, cry, get dirty, and run miles every day carrying pounds of gear, DON'T JOIN.
MP's are Marine Corps and Army. Security Forces (SF) are Air Force. Navy only has security for ships, which I believe you must hold a higher rank for. Coast Guard has law enforcement as well. You will not only be patrolling. It's not that easy of a job. You will also handle domestic issues on base, issuing speeding tickets, conducting investigations, and handing out citations. You could also guard checkpoints on the base. I have friends in MP (Army) and they can attest to this. Also, being an MP your only friends will be other MP's. Other people tend to dislike you for messing up their fun.
You are deployed whenever the military needs you. You have NO say in it and you have no clue when it will be until you get your deployment info. You also have no choice where your first duty station will be. The military decides for you. I'm pretty sure you can specify what you'd like to have (i.e. in-state or abroad), but that only serves as wishful thinking. I've had friends choose in-state and be assigned in Italy. I've had friends choose abroad and be assigned to the same base where they used to live close to. Never join because you want to go to a specific base or be close to family.
Yes. You would be in the active National Guard...you would be required to attend drill at the assigned base one weekend a month. However, you will have to go to training 2 weeks out of the year. You will be getting pay ONLY for the drill weekends, not nearly as much as active Army pay.
Honestly it doesn't seem like the military would be right for you. Every single occupation across all branches are DANGEROUS. You do have the possibility (a very high one at that) to go to war. You wanting to join a combat arm conflicts with your desire to not be in dangers way. Keep that in mind.
