It all depends on what you mean by a "secure site". If you need SSL for e-commerce, or other "encrypted" or https functionality, then you will need a hosting plan, a fixed ip address, and a certificate.
However, if I read your post correctly and all you really need a a place where you can store your files "secured" from public view, and only available via a user/password combination, then any DH plan with sufficient storage/bandwidth for your needs will work just fine, as you can use apache authentication to restrict access to the site/pages/files, etc. with no additional cost.
Prices are clearly stated on the Dreamhost.com website - with the primary difference between the first 3 levels of plans being quotas. It is quite likely that the lowest plan will be sufficient depending upon your storage/bandwidth needs.
You can pay by the month, or for a discount, by the year (with waived set-up fee) - when you add it all up the 1 year plan is a better deal.
edit: Upon re-reading your post, note the Dreamhost Terms of Service if you are planning on hosting video files - as DH is U.S. based, you will be subject to copyright/DMCA restrictions regarding what files/videos you store on DH - just a word to the wise.