Compressed Export for fullsize Hero Web-Movie

Hey,
I'm very new in «editing movies». Maybe anyone could get me a hint, where I can read some stuff about export with strong copression for use on websites...

I can't find usable search-results from Google nor from this forum-search-tool.

Would like to produce some background-hero-move like under: campaignmonitorDOTcom.

I tried in DaVinci Resolve «Deliver» with Youtube/Vimeo-export presets also different manual settings.
But at the end, a 24s Movie like that above is not little 2.9M.
- Direct from DaVinci Resolve 24s with 1029x1080 24f/s H.264 QuickTime : 59M.
- After Recalc with ffmpeg to mp4 is down but also tooo big for web: 37.5Mb.

Hope someone have an advice to export some move to files as little as possible direct from Resolve or maybe to compress afterwards with ffmpeg or other post-production stuff as much as possible, to try different sizes/qualities...

Would be great to get some hints!

Thanks Martin

Found workaround-tools with Handbrake and VLC.

But I guess, smaller input will get smaller end-file-size ...
Maybe anyone have an advise what settings are best for the smallest mov-export in DaVinci Resolve. So at the end I get as small as possible compressed/converted files from from Handbreak/VLC?