Are you just trying to become a paralegal?
I had a business contact who worked for a company that did headhunting in the legal field. They also placed temps (lawyers, legal secretaries, paralegals) and did temp-to-perm placements. It was her recommendation that paralegals get a paralegal certificate/degree from a paralegal school which was
certified by the American Bar Association.
If you're just becoming a paralegal, I strongly suspect that law school will cost more than you will recover in extra pay. While law school will give you a far more thorough education, lawyers don't expect paralegals to understand the law that well.
I work in litigation support. While our team has a few members who went to law school, most have some sort of financial background (accounting, business, economics, finance). New employees learn the relevant aspects of the law on the job.
But it really depends what you want to do.