Your site will be hosted on it's own virtual private server. I buy from multiple providers, but all have at least 512 MB of ram, and can handle at least 25k daily visitors provided that your site has static content (like this one). You can test the speed of the server this site is hosted on by downloading this file: http://static.dustinhess.com/100MB.zip
The server itself will be the most recent version of Debian Linux. The server will be running the Cherokee web server and a MySQL database. I will ensure that it's kept up to date, and will notify you if there needs to be any maintenance done to it that will require any downtime. Optimally, downtime will be less than 5 minutes a month for the rare update that requires a reboot.
The backups will be taken every 24 hours, and transfered to a server that I run in a different geological area.
I can provide you with a shell account that can be used to ssh/ftp to the server. There will be room for at least 5 GB of static content (pictures, documents, and downloads).
Video hosting is done through Amazon S3. S3 is billed on a usage basis, and they charge for both storage and bandwidth. Typically, if you want to host videos, I will help you get a Amazon S3 account setup under your Amazon account and we map it to a subdomain of your site (videos.yoursite.com). Typically, I will borrow your amazon credentials to do all the initial setup, I provide you with a quick tutorial on how to upload content, and then you change the password to the account. This setup allows for you to host all the videos or large files you want, have them not impact the speed of the rest of your site, and you have 100% control over the videos you want to share. S3 has no limits on how many or how long your videos are, and expands to provide enough capacity for millions of views.
Here is Amazon's S3 pricing:
http://aws.amazon.com/s3/#pricing
If you have any other questions, just send me an email.