JigsawPuzzler

I was admitted to Cal State University, Dominguez Hills this fall for the Computer Science Graduate Program. I applied to this program specifically because they were one of the most flexible in terms of academic background. My bachelor’s degree is in history rather than computer science. CSUDH offered conditional admittance, and only require that I take some prerequisite programs in order to change my status to fully admitted. My question is how important is the quality of the school for job prospects? CSUDH is not one of the most prestigious schools and the classes already feel somewhat remedial. I’ve basically set my own standards to do extra work in order to understand the subjects better than what simply getting an “A” in the class would indicate. I’ve even considered using this degree and school as a starting point from which to eventually apply to a PhD program at a more prestigious university. Is this necessary? What advantage would that provide me?