Is there a way for me as admin to receive an email whenever staff members have updated the site?
Actually, it would be really good to know when a contributor has created a draft or updated it. So that admin or editors know they need to check the draft and publish it.
You should use Webhooks for this. Ghost Webhooks
post.added, post.published, post.edited and post.scheduled are the events you might be interested in.
Here is a useful article as well.
I think you could also use Zapier for this. Same idea as a custom integration, but you don’t need to manage the webhooks yourself