The best route is probably attending a local state school that the office(s) you are interested in recruit / hire from.
Difficulty of getting an ADA job largely depends where you will be looking for the job but also other things like how many new lawyers the office will hire, whether that office is under a hiring freeze, etc. It all depends. DA offices also care about grades in law school. They aren't going to be looking at candidates in the bottom half of the class. Also, be advised that many DA offices will not hire until after you pass the bar. That means you'd half to pass up any job that might hire before school ends (big law firms, some govt positions, etc.).
Whether or not you qualify for an LRAP program will vary from school to school. There is no standardized LRAP progam. Some will not cover DA positions at all, but only things like legal aid. A word of warning: many LRAP programs do not have favorable terms. You will likely not be able to save any money or own any property, and if you get married, your spouse's income will likely factor into the eligibility calculations.