Hello TEKHD and welcome to the forums.
First of all congratulations on your new Capital One card. And to answer your question, no, you DO NOT have to pay interest in order to improve your credit score. It might be a good thing for the bank because they are making money, but paying interest has nothing to do with improving your score. If you have the money, just pay in full whenever you can and save yourself the extra fees!
The two most important things about using a credit card are:
1. ALWAYS pay on time!
2. Do not max out your card!
Just make sure you do not pay late even if you are just paying the minimum. ALWAYS pay on time! Paying late looks bad on your report and affects your score (even if it’s only a day late!). Also, do not max out your card. Some people say you shouldn’t use more than 30% of your available credit at any given time, others say 40-50%. Play it safe and keep it on the low side.
Here’s an article with some good tips on how to improve your score: http://www.myfico.com/CreditEducation/ImproveYourScore.aspx
Hope this helps!