If you are seeking an engineering job, do employers care about which university you attended? Do they look at your grades, or bias their decision based on the college's reputation? There are stories of Ivy League graduates struggling to find employment, while another person at a small, virtually unheard-of college grabbing that opportunity. So if you are attending a prestigious school, and your grades are lower than someone who is attending a small, high-school-like school, how will that affect your employment opportunities?
If you are seeking an engineering job, do employers care about which university you attended? Do they look at your grades, or bias their decision based on the college's reputation?
If you have a solid foundation in the skills that matter for your engineering discipline/sub-field, and can convey that to recruiters in a phone/on-site/on-campus interview, then I would say that to a first-order where you did your degree does not matter so long as you can get the recruiter's attention.
Getting the recruiter's attention is the trickier part for those coming from lesser-known schools. For example, at the engineering schools I'm familiar with, new grads can find a lot of good fresh-out career opportunities by attending on-campus engineering career fairs and the like. The downside of attending a lesser-known engineering school is that they may not have a decent attendance of engineering companies that come to the campus for recruiting purposes in the first place. This puts the burden on the student in getting a recruiter's attention.
Engineering students (and students in other fields, I'm sure) from any institution can greatly benefit from networking with peers at other institutions and those already in industry. For those from lesser-known institutions, networking can be an invaluable tool for opening doors to career opportunities. Also, while obtaining an internship may be equally as difficult as obtaining a full-time position for those from lesser-known schools, participating in several internships along the way to obtaining your degree if at all possible (and performing the duties of the position well) would really go a long way to improving your chances of success.
Many firms tend to prefer certain schools -- drawing exclusively from CalTech or from MIT, etc. Some hiring managers tend to feel that this builds coherence and loyalty within the engineering ranks.
(Heavens forbid that you put an MIT engineer with a Caltech engineer on the same team unless you want to have them compete against each other.)
Some hiring managers have intense loyalty towards their own school and want to promote their own.
Others simply choose the best available in a specific domain.
It all boils down to the hiring philosophy of the company.
My own advice is that you should choose the program that you feel has the best fit with your interests. There's no point in going into a 'good' program if it's weak in your own area of study.
Does it matter: yes. Everything matters. Next question please! Upvote at your leasure!
The question you should ask is "How much does it matter?"
The answer really depends on how well you know your field. A brand-name school is most likely to help you get through an initial screening, but unlikely to land you the job. If you're on the fence, technically, and you need a large number of interviews to land the job, a brand-name school may be the ticket you need. On the other hand, if you actually know your stuff, you won't be so dependent on "good luck" in the interview, and you can afford to get missed in the screening once or twice... all you need is one interview and you're set!
Alternatively if your activities stand out, you wont need the brand-name school to sell your way past the screening process -- what you've done will speak more than your alma mater.
Traditionally, yes but more and more companies are beginning to move past that. Government jobs however are different. They would select based on school and also background.
But, anyone who has worked in a diverse environment would know all that very surface level. Engineering is all about finding solutions to problems. It always depends on the company's business model, hiring policies, alliances and other factors. It is not as clear cut as school where an A is an A regardless of the person getting it.
The whole "go to a good a school, graduate and get a good job" line is very misleading. It might work out for a lot of people (especially back then when a select few go to college) but do not depend on it to work out for you (unless daddy's the boss, then why are we even discussing this). Depend on yourself first and keep at it till it does work out. It sucks but you will be able appreciate every bit of it much better than you struck gold at first strike.