Here is a bit of advice strickly coming from my own personal perspective. I would discourage you from getting a criminal justice degree! What, you say? Law enforcement agencies are looking for good solid responsible, thinking entry level people. They do not expect you to have any law enforcement experience. You will learn everything you need to know about "police stuff" in the academy and field training. I would rather see you get a degree in something that is more portable in case the law enforcement thing doesn't work out. You may get injured, don't like it, or just not be cut out for the job. At least you have a degreee to fall back on. There are many other degrees that will ultimately help you in both law enforcement and the public sector such as: sociology, business administration, computer science, public administration, teaching, psychology, etc. All of these areas will be applicable to law enforcement especially if you are interested in climbing the ranks.
Law enforcement has been a great carreer for me and I wish you well,