<p>To start some independent research, first look through the faculty profiles to see their research interests. You'll want to find someone in an area that interests you. Next, look at the person's CV. You want to find someone who has published in the last year or two (some people get tenure then stop publishing - they focus on teaching, college administration, etc. instead). You probably also want to find someone with tenure (Associate Professor or Full Professor). Tenured professors make better references, are more established in their field (usually) and are also under less pressure. Untenured faculty are under pressure to publish, publish, publish, so they often won't work with undergrads (or in your case, not even an undergrad). Tenured professors usually also have more experience with student researchers.</p>
<p>If multiple people meet all those criteria, then Google the names on the CV where the person lists his former students / PhD committees. Look for a professor who has placed students well (his students are hired by top universities). That mean's he is well connected.</p>
<p>Finally, find a person that it seems like you can get along with. Not so important for independent study, but good none-the-less.</p>
<p>Once you've done all of that, read the abstract from several of the person's papers (you should have done this in step 1), then just setup a meeting with the person, tell him your intentions, tell him that your goal is grad school (or at least make him think that). There you go. If you get rejected, try someone else.</p>
<p>And start with the engineering department.</p>
<p>As for "why MIT and not NC State": you're going to get very different salaries coming out of those schools, ceteris paribus, but I bet your goal isn't industry, it's grad school. After grad school, no one cares where you went for your undergrad. So if you can go to NCSU, finish with a 4.0 GPA, and get into MIT, Stanford, or GT engineering afterward, then it doesn't matter. You will be more challenged as an undergrad at MIT than at NCSU, though, and if you finish with a lower GPA (in the 3.5 or lower range), the MIT bump will help with admissions. </p>
<p>Forget money - with graduate level coursework, most schools will give you a scholarship.</p>