Background Video - Full width and high resolution

Hi all, 

I have a video background for my cover page.
Unfortunately, it is blurry for the first 5 seconds or so and given this is a website for a Director, it's important the quality is of a high standard from the start.

I would like to know solutions for:

A) Making sure it plays high quality from the start
B) Making sure the video defaults full screen so It doesn't need black bars (For both desktop and mobile)

Any help greatly appreciated.

Thanks