Though, Mercurial doesn't have a particularly great git-export story, so syncing to GitHub or the like is harder. (Fossil has a better story there, with first-class git export, but a different workflow, and harder integration story (a RESTful JSON API)).
Git tends to be harder to integrate with, as there is sort of an expectation you'll maintain a shell process for it. [1]
As to zipping, with Git, you need to zip the whole repo.
Fossil can zip files upon storage, or you can zip the *.fossil file.
Mercurial can bundle with gzip, to simplify things a bit.
My point being, though git can give you some nice places for users to deploy to, it can be a bit of a pain to work with, and a couple other SCM systems might need to be considered. They might make your life a lot easier.
[0] https://www.mercurial-scm.org/wiki/MercurialApi
[1] https://git-scm.com/book/be/v2/Embedding-Git-in-your-Applica...