What are the best options to convert video into gif in high resolution?

on website I need to put a background video.

Embeded video is not an option for me, as it has problems with autoplay on mobile.

And actually, as I don't need to control it, I decided to create a gif from this video.

I want to create several gifs, depending on screen resolution in order to optimize website loading process.

Can you please recommend me services, where I can convert 1080 video into high resolution gif? And what is an optimal size for background gif?