By the time you finish law school, you'll have forgotten almost everything you learned as an undergrad.
A political science major is pretty versatile. I had a lot of friends with them and they did everything from selling heavy equipment ($$) to working for congresspersons ($). A bunch of them went to law school. One is a corporate financial advisor in Manhattan. A few are probably selling real estate or insurance somewhere.
I double-majored in Philosophy/Political Science before going to law school. I was one of only two Philosophy students in my class at U.T. that went to law school (the other phil. majors thought we were back-stabbing, capitalist pigs). I had been a business major my first two years, so I did take a lot of accounting, economics, statistics, bus. calc., etc., before switching over. I personally wouldn't go the criminal justice route before going to law school. You can learn all you want about criminal justice in law school, especially if your school has a clinic. If I could do it all over again, I would seriously consider an engineering degree and patent law. I'm still pretty happy with my choice of undergraduate study and would suggest that a good philosophy program is a very beneficial background for becoming a lawyer.
Some of the more successful young lawyers I know went to schools that weren't too hard, and majored in stuff that wasn't too hard so they would have a super high GPA. I didn't know it at the time, but this really works. At least it did when I was applying to law schools. A 3.65 GPA in Elementary Education from Middle Western John Doe College beat a 3.1 GPA in Philosophy or Finance or Biology from U.T., Michigan, U.C.L.A., etc. No weight is given to how hard your course of study is. Basically, the only thing that counts is your GPA and your LSAT. I don't think anyone even reads the other garbage they have you submit. Same thing applies in law school. If you want to interview with the top paying firms, you'd better be in the top 5% of your class. I was not. I do not make a lot of money practicing law. Im still paying for my legal education and will be for a long time.
If you just sorta think you want to go to law school, or some relative recommended it and you figured it might be something to do, forget about going unless someone else is paying for it. Find a good school (like Rice) and study what you want. If you approach law as a profession that might require something to fall back on (and it might) you should not waste your time with it.
If youre passionate about becoming a lawyer (you named your dog Atticus, built the scales of justice in shop class, and mediate family discussion at the dinner table) then you should figure out how to make really good grades in something as an undergrad, kick ass on the LSAT, and get into a good law school. Youll figure out what to do from there.