Rank isn't so much the determination of pay as is the rank of the mission they are going on. D and C-Rank missions, have lower income, but that just means Genin need to do more of them in order to pay for their expenses, living expenses or anything else. In the anime, it is shown that a traditional Genin can make enough to support themselves, almost like minimum wage worker, but supporting a spouse is more difficult, and children is almost out of the question.