"Webpage for video upload" will actually upload the video to the web server. That's just the way HTTPS and an HTML form with a file-upload works. Make sure to set the right content-type on your form tag properly for a file. You cannot send other parameters to the server with the same request as a file upload because of that same content-type parameter. A big problem may be people with big files and/or slow internet that keep your HTTP connection open for 15 minutes or more. Most people's ISPs have a maximum upload rate of 500Kbps (bits/sec, not bytes/sec) or something really low like that. Long connections make you a target for DOS attacks.
If you want the file to end up somewhere other than your web server, you'll be writing code on the server side. Your web application will have to pipe/stream it to that different location.
FTP is very slightly faster than HTTP, maybe 5-10% max, but I think my experience shows it's closer to 1%. FTP might be better for transferring 2 or more files at the same time, I don't know. I think all modern browsers support FTP natively as well as HTTP. To use another protocol as someone suggested, you need server side code. I'd use HTTP for your first pass.
Someone raised a good point about encryption. You want that if anyone will send confidential or non-public video. It will slow things down somewhat, but probably not that much. HTTPS with a server side certificate will take care of that if you need it.
When transferring large files, you need to use a protocol that ensures that they are not used by the recipient until the copy is complete. Maybe you touch another file, or send a "all-done transferring myFile2321.avi" message. Compressing large files and decompressing them after the transfer is often faster than copying them over a network or the internet. If you pay for bandwith it may be cheaper as well.
So, all in all, those are some details to think about and some suggestions. I don't see anything wrong with your over-all plan. Take a look at how YouTube does this, because I think they already do everything you are planning, just in a different context or for a different reason.