Good question. Either path is a good path. I am partial to the military path, however.
While going straight to college definitely has its advantages, enlisting in the military is a great way to go for several reasons.
1. You will get to experience the world as a young adult. Many young people don't get this opportunity otherwise. It builds confidence and character.
2. The military offers the GI bill for educational purposes which will follow you into civilian life even if you decide to get out of the military after you've served your term. For example, my husband was Air Force. His GI bill paid for two Associate degrees, a Bachelor degree, and two Masters degrees. It was very much worth it!
3. If you want to be a police officer, I recommend choosing Security Police as a military job. Security Police is the field of law enforcement in the military - at least in the Air Force. You should be selective, though. There are two types of Security Poiice in the Air Force: those that deploy and those who stay back to guard the base. My husband was assigned to the unit who stayed to guard the base and this is most like civilian law enforcement. He did deploy on occasion but not like the other units. Either way, though, both will give you great experience and moving into civilian law enforcement later will be an easier transition.
I'm happy to answer more questions for you.