For a "decent" job, it doesn't matter; for the best jobs (or cofounders!), it will be helpful to start off at an elite institution.
The most important qualification for getting a job at a place where you can be happy as a software engineer is the ability to quickly write short programs at the whiteboard while your interviewer looks on and takes notes. You'll be given a problem statement and expected to identify an efficient combination of basic datastructures and algorithms to reach a solution on the way to writing down the code and discussing its correctness and the merits and demerits of the choices you made. You really don't want to work at a company that thinks a formal credential is more important than actual ability.
The reputation of your school doesn't matter much outside of first-rate software companies, where it will be helpful but not necessary to have a top-5 school on your resume.
Having said that, a major benefit at a strong school is that you'll be among the people who wind up working at all the best companies. It's good to learn and work with talented/motivated/smart people, and it will be easy to choose good internships and good prospective employers because you'll know so many people with first-hand knowledge of each place.