Double majors, undergrad research, best college worth it?

[xcvxcvvc]

I have several questions. I'm working to earn a BS in electrical engineering, and I will finish before four years. Now, I have scholarships that pay for my education for four years.

1.) Should I pursue another degree to use the free education? It'd delay my transition to graduate school, and I'd need to pay for some of the education, meaning it's not completely free. I'd have about two semesters of free schooling and be left to pay the rest. I'm going to a mediocre, local university, so the cost would be only about 5k per semester afterward. If so, which degree should I choose? I was looking at either computer science or math.

2.) I'm talking with one of my professors about undergraduate research. Is that a good idea? Do graduate schools or businesses pay attention to this research when considering candidates?

3.) I'd like to earn my masters and maybe my PhD from the best college possible. Is it worth the enormous price increase (relative to my current school) to earn a degree at a more recognizable name (assuming I can even get into a better school. Currently, I have a 4.0, am studying for the GRE, and have prospects of undergraduate research)? On my current track, I'll have a masters without any debt. Leaving the state to attend the best name that accepts me would probably accrue tens of thousands in debt and leave me feeling homesick at least momentarily.

 

[Knochera]

I can only speak to your second question, and from a physics major's perspective rather than EE. That being said I know that research is a huge part of getting admitted to a graduate school (at least in physics). Some would say its the most important factor actually. So yes -- start as early as you can with it and take it seriously. Try to get as much work done in your research as possible if you are aiming for graduate school. The more you can show off what you've done, the better chance you'll have at getting into the program you want.