You could discuss the company's vision, culture and solutions/services as reasons for wanting to join it.
Pick three adjectives but then back up each with a real life story that demonstrates those characteristics.
Understand that companies invest a lot of money into hiring the right staff. You want to emphasize that you are in it for the long run and you want to develop a career there and that it's not just a "5 month stepping stone" type of a job. You should be thinking how you're going to grow with that company. After all, don't you want to invest your energy and time with a company that is going to continue to be successful and one that will help you grow?
Make you give an example where you discuss details and metrics. For example, I was a tutor in my last job and mentored 5 students on their SAT test taking skills and raised their scores by 15% on average after a 3 month teaching stint.
Talk about a story / experience about how you achieved success and be sure to share details on the results and outcome. Have it highlight a strong characteristic such as leadership, work ethic and so forth.
You should be proud of all your achievements! We just don't have time to hear them all as interviewers most likely. Focus on 1 really good achievement that showcases characteristics like the following: Integrity, competitiveness, resourcefulness, intelligence, persistence, and so forth.
Describe your charitable activities to showcase that community work is important to you. If you haven't done one yet, go to www.volunteermatch.org - charitable work is a great way to learn about other people and it's an important part of society - GET INVOLVED!
Don't try to sugarcoat the answer by listing something ambitious as a fear, unless you truly mean it (for example: I fear being a great leader) - Share your real fears but discuss how you would overcome them.
If you want to show your fun side, discuss your extracurricular activities. If you want to show your ambition, discuss the work / school projects you do in your spare time.
I would weigh the offer and consider it, however, this company and this role is my first choice.