Videos, sizes, web and mobile

I’ve been reading up on delivering video content and though I’ve learned a lot, it still feels like the wild west. There are just things I can’t seem to find answers on. I’m looking at utilizing the HTML5 video tag and having the 3 formats to cover most devices. I think I’m good there.

Where I struggle is on video sizes, resolution and scalability. My boss is wanting a great big video on our site. Almost 900px wide. It’s for a new product we have, btw. I’m not sure we need it that size, but my real concern is how big of a file that will be and how slow it could be for some users. Then there is the matter of mobile devices viewing the video.

Do videos scale down for mobile devices? Do I need different size videos for different devices and different internet speeds?

I used to see Apple’s movie trailers give options on playback size - small, medium, large. I thought that might be a solution, but I’m not finding that so much in use any longer.

Can anyone shed some light on video sizing for me.
Thanks for your help!!!