I'm not a web developer, but hopefully I can point you in the right direction. If you're comfortable with Python, then I can point you to the popular Django[1] web framework. Though really, if you've barely used Python, then it would probably be equally easy to get started with Ruby and Ruby on Rails[2] instead. Like I said, I'm not a web developer, but I know both frameworks have lots of support and information out there, including tutorials. I highly recommend following through with some tutorials first, just to get yourself accustomed to how the platform works.

As far as your actual idea goes, I saw the keyword "privately". Now when you first start out and it is just you and your girlfriend, then privacy is easy if you two are the only ones who can access the site. Presumably other people would also want to make sure that not even you, the site administrator would be able to view their uploaded videos. That is probably going to mean encryption, and the mess that comes with it. Colin Percival has a recent blog post[3] about designing apps and services so that the users don't have to trust the developers.

In the meantime, a quick and dirty solution would be to have a Dropbox account that the two of you share, so when you place a file in the proper directory, it automatically gets synced to the other person. You could even encrypt the videos locally before putting them in the Dropbox folder. (You'll probably have to move them from the Dropbox folder to elsewhere after the sync, or you'd quickly fill up the 2GB limit for free accounts).

[1] https://www.djangoproject.com/ [2] http://rubyonrails.org/ [3] http://www.daemonology.net/blog/2012-01-19-playing-chicken-w...