Thanks all, right now testing Cloudflare free service.
But still plan to use Dropbox for some projects. So if someone will
find a solution to set cache headers for Dropbox, plz share)
As for Dropbox bandwidth limitations what I found seems to be quite
enough for me:
"public links for free accounts may not use more than 10GB of
bandwidth per day while that limit is 250GB per day for paid Dropbox
accounts. The links are automatically suspended if any of your files
exceed that limit."
Proper caching will also help to stay on the safe side.