This is a fairly long post with multiple typos I am procrastinating on work I should be doing and do not have time to proofread so please excuse the typos.
Before I say anything realize anything you read on the internet from anonymous posters myself included should be taken with a major grain of salt. I never been to Duke or the South so I can't discuss with any sufficient accuracy what is best for your situation.
However, I do have friends that obtained Big-Law jobs, it never interested me in law school, but there are the basic steps which you already know.
1) DO WELL IN SCHOOL:
Most big law firms only hire the top students, but unfortunately only 10% of students can be in the top 10% and this means there is a 90% chance you will not be there. This is not a knock on your intelligence just a fact at every ABA school across the country 100% of students think they will be in the top 10% and every year 90% of students are wrong.
That is option 1, but I imagine you knew that.
2) OPTION 2 THIS WORKED FOR A FEW FRIENDS IT MIGHT FOR YOU:
Since law school is not going to start for a another 6 weeks and you have some free time go to firm websites your interested in. Look for Duke Alumni working there and send them an e-mail asking for an informational interview just to make contact. (Do not Ask for a job on this, but just come prepared with some questions and if they allow to come to their office and meet people that is great.) As a OL there won't be the pressure of needing a job now and believe it or not a lot of lawyers "Love to talk about law school ideas and so forth" hence my continuous posting on this site.
If that goes well keep in contact and briefly and when 1 or 2L summer is coming send in the resume and at least they will have a face to associate the name instead of being one of a 1,000 other applicants. Doing this can also show a little more initiative on your part and makes you stand out.
Do not be pushy with this just send a proofread e-mail to attorneys at firms your interested in. Duke has a lot of alumni working in big-law jobs so seek them out specifically they might even give you an outline for a course or something.
-Or they simply will not respond and you have lost nothing-
3)OPTION 3-BAR ASSOCIATIONS
I am pretty good at sports and I joined my areas Bar Association which had lawyer leagues for soccer, softball, stuff like that. Usually there will be a free agent team put together which you can join and meet some people that way. I never expressly asked for a job from anyone, but they would ask how school was going, give me advice, tell me about the struggles with the bar, so and so on. This helped me know a lot of lawyers in my area and they helped me out when I was starting.
You may not get a big-law job through this or any job at all, but getting to know people face-to-face and having them like you is much more important than getting an A in contracts or going to the 12th best school instead of the 19th.
Every city I have been to has a bar association and I imagine whatever county/city Duke is located in would have one sign up for that and it may cost 20-30 bucks it is fairly cheap for law students and engage in the Bar Association activities.
It also doesn't have to be sports the bar associations throw all kinds of events and you can meet people a lot of people this way.
4TH OPTION AND NOT NECESSARILY FOR BIG LAW, BUT FOR YOUR CAREER:
Before I enrolled in law school I had a lot of non-lawyer friends and I kept them through law school. Many law students leave them behind, but I kept them first because I liked them and second whenever they needed a lawyer they would ask me for help. If you have your own book of business it makes you quite valuable and you can go anywhere with that.
My main point here is that every connection does need to be with lawyers keep yourself well rounded and around those that were there before law school. As most recently minted J.D's find out the first few years are not as glamorous as Franklin & Bash, The Firm, etc make it out to be. It is a struggle and keeping yourself close to people you knew before law school will be good emotionally and likely for your career success as well.
Again these are just some ideas that have worked for me and others, but you may have a different style and there is probably some other solid advice out there that would conclude this is wrong. Use your best judgment throughout law school and never forget your common sense.
Good luck and congrats on getting into law school!