I'm assuming you want to do it on the cheap: 1 minute of video isn't long, you might only be just commencing this idea, and once your website is running you might want to redo the video again anyway to better reflect the message you want to convey.
Two options come to mind:
There are a lot of companies that provide this type of service. They range in price greatly from 4k to 20k.
You can see a lot of options here http://www.quora.com/What-are-the-best-studios-for-producing-explanation-videos-like-Epipheo?q=epipheo.