Staging Sites: What to push through?

I have a staging site where I am improving the theme and layout, adding a couple of plugins to add a slide in navigation bar etc. The issue is that on the live site, people are signing and purchasing membership, plus some memberships are expiring etc. Oh and I’m with siteground.

My question is, how do I push through my staging site so that the users’ data on the live site persist? Is all user data stored in the same table? When pushing the new site is it possible to only push through the database tables that I have made changes to due to my development, leaving all other tables in tact from the live site?