You might want to look at a video streaming service like Vimeo ou YouTube

Totally agree with @lrnlab , not only for file size issues, but for handling streaming, multiple devices, accessibility, etc. it’s usually a great idea to use some type of dedicated video streaming service and then embed in courses or on pages instead, unlisted YouTube is always the free go to for folks, but Vimeo, brightcove, Kaltura, etc. all provide great company focused services to own and customize the data. If you must just compress files, get a good video editor like Adobe premiere or davinci resolve to be able to control the output settings and play with the bitrate to crunch it down as much as possible without losing clarity. Can always use something like Handbrake to do that too but not as much control. 

Where I agree…you may want to try the freebies handbrake or Adobe media encoder.

Handbrake is a long time well documented video encoder that helps in this space.

Adobe Media Encoder? Has helped in the past but I find Handbrake is my go to.

By the way - there are sooooo many video streaming solutions out there…and articles about them….I am sure you will find one that will be cost effective for what you are trying to do.