What is MMA? Is that Martial Arts?
If that is what you mean by MMA, then there is no specific job for MMA.
You may or may not stay in the United States if you join any branch of the military. I spent a lot of years overseas...and loved it. It was a little scary at first, but I learned to love it. Japan is a cool place to go.
All the pay and benefits are about the same no matter what. A private in the Army and a private in the Marines gets paid the same.
Nobody wants to die unless they are crazy. If you don't want to go to war or go overseas get another job. It is like a fire fighter who doesn't want to go in a burning building. Military is for war fighting, and defense of our country. You may not be on the front lines, but you job will somehow support the war fighter...that is what the Marines and Army does.
I was Navy. You could join the Navy and be on a ship of the coast of a war zone. But it can be dangerous too. I didn't have to go to Iraq while I was in...I went to Guam.
You don't always pick where you get orders, in fact most of the time you have very little choice.
I don't know anything about cage fighting. I don't even know if there are competitions among the military...you would have to check. It sounds like something that you would have to do on your off duty time, if you are allowed to do something like that. You would likely need permission to fight because of the danger of getting hurt. I know that there are boxers and other compete fights as sports...but I haven't ever seen any military competitions. (I haven't been everywhere either...but if it exists at all you would have to look it up.)