Cheating death and fighting communism: that is how a fellow officer once described our job.  It was meant to be funny, but as time went on it seemed all too true.
I spent more than ten years in law enforcement, all of it on the street in uniform patrol.  I've been a patrol officer, instructor, sergeant and lieutenant. 
Do not report crimes here. Nothing here should be considered legal advice. All opinions are my own.
                             If no evidence exists, and no witnesses have presented themselves, then what additional actions would you suggest the officers take (within the confines of the law)?  Maybe your neighbor did it, maybe she did not.  People should never be arrested for "maybe."  
IF you neighbor damaged your tires, and IF she admitted to tampering with your mail, it sounds like your best bet is to file a report with the postal police and see if they develop probable cause to arrest her.  IF they do, then her probation can be revoked also.  
It won't likely keep her in jail for very long, regardless. 
                          
                             Get good grades, stay physically fit and stay away from drugs/alcohol/trouble.  I was in high school too, but all of those things will play a role in your hiring process.
If your local department has an explorer program, check on joining that.  It will give you a good amount of experience around police officers and get you some training (plus a foot in the door when you apply for a job.)
Personally, I'd avoid any kind of criminal justice/criminology degree.  Stick to some kind of degree that can make you money - business, computer science, etc.  Don't waste time and money on an expensive degree or go into debt for it.  College debt is a trap.
Can you take college classes while in high school?  I know here in Florida, juniors and seniors can often take college classes and get dual credit:  high school and college for the one class.  I managed to get several of my college classes done for free before I ever left high school that way.
Joining the military (any branch) will help you get hired later and will help pay for advanced education.   
                          
A detective will generall drive an unmarked car provided by the agency. The type of vehicle varies greatly. I've seen everything from a Prius to a Mustang. Most departments will go with a domestic sedan, though that is not always the case. Sometimes the detective's job will dictate the need for a different kind of car. For example, a narcotics officer will not be driving a Crown Vic. Sometimes a vehicle might be seized through civil forfeiture and be used by detectives. Unless you think the car is integral to the story go with a Ford Taurus or Chevy Impala.
I'm not familiar with Colorado law in that respect. If you call the local Sheriff's Department, they should be able to tell you.
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                             It depends on the size of the department.  For any agency of more than about 15-20 officers, the chief is not likely to be involved in any case other than as a spokesperson in a high-profile incident.
For small agencies, a chief may patrol and handle calls like the rest of the officers.  There are many departments in the US where there are fewer than five officers.  In those areas, the chief handles a lot of the calls and investigations. 
                          
                             I do not have a military background, but it looks like the USMC has a variety of law enforcement related MOS: http://en.wikipedia.org/wiki/List_of_United_States_Marine_Corps_MOS#58_Military_Police_and_Corrections 
That said, I've worked with plenty of officers who were former miltary that did not have a MP background and they did very well in the hiring process.  At my last department, I worked with a former Marine who was an aircraft mechanic, another who was in motor transport and a third who was a machine gunner.  All were good cops.
If there is something specific that interests you, go for it.  If you have a solid service record and even manage to get yourself promoted, it will all work to your benefit when you apply for a civilian law enforcement job.
Remember your oath, stay safe & thanks for your service. 
                          
                             Detectives can participate in a warrant service, and frequently do.
A high risk warrant service is usually handled by a SWAT team, which can have detectives on the team.  Once the scene is secure, non-SWAT officers/detectives will frequently be responsible for the securing and documenting of evidence. 
                          
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