There are too many options. There are 725 plugins tagged video for WordPress. Not all of these will work with BuddyPress.
https://wordpress.org/extend/plugins/search.php?q=videos&sort=
You are better off testing plugins out. As for themes, you can use most WordPress themes with BuddyPress but you will have to adjust the code.
Theme, you can get a WordPress theme with magazine format then install BP Template Pack which you will need to tweak to mesh with HTML structure of your WP theme.
Photos, videos and audio (if you allow all three in admin) uploads working with BP Gallery Plugin, which is premium at this time. You could set Gallery page to include all media or set up pages for respective media. Edit – Also individual members plus groups have their own respective photo, video and audio gallery pages out of the box.
Also check out the well-supported themes by the wpmudev.org group… they cost, but they will provide fantastic support and are guaranteed to work with all upcoming BP updates… Agree with @modemlooper …. the beauty of BuddyPress is you can do anything… the caveat with that is you have to spend a lot of time figuring it all out, trying things, and you might even need to learn a little “programming” along the way to make it do what you want…
http://buddydress.com/themes/
