Hello,
I have read your requirements and they are pretty clear to me. Going for embedded content would mean your server resources remain pretty low while using the service of an already established platform specifically designed to scale their resources depending on the server load.
One question tho, this webinar platform, will it be like a directory where I could consume the api provided by vimeo/youtube? That would be best if you plan to go with my services.
For building the actual platform, I suggest going with something like laravel/codeigniter or one of the cms solutions developed for them. Sure, you could choose wordpress, but wordpress is rather unwieldy on scaling.
Looking forward to hearing from you.
Regards,
Adi Oporanu.