If you want to download or stream music with Out-of-the-Box, you will stream the files directly from Dropbox. So there are no bandwidth or file size issues for your web host. Only when you download zip files, these files will be downloaded to your site and can generate some traffic.
Dropbox API uses its own bandwidth limits. For Free accounts, the total amount of traffic that all of your links together can generate without getting banned is 20 GB per day. For Pro and Business accounts, the limit is 200 GB per day.
So if you have a lot of visitors and you have plans to use large video's or have loads of images, you should probably upgrade to a Business account.