Need child theme help

I’m trying to get a child theme of weaver-ii setup on multisite for a non-profit charity so that it’ll be easier to make the main site and the subdomain sites (chapter location sites) look consistent. I am new to both multisite and child themes.

I’ve made a directory and style.css for the child theme; however, the style.css of the parent theme (weaver-ii) says that it uses style.min.css. So, do I make a style.min.css file in the child theme directory in addition to the style.css? If so, is it done the same way or do I have to look for more info to change to the child theme?

Basically, I want all of the sites to have the same background and color scheme (that I’ve changed within weaver-ii admin options, before trying to create child theme) for menus, widgets, etc. I would like the header image to either be the same or, preferably, be a different image that includes the chapter name for the subdomain.

I’ve read just about everything I can find about child themes and I’m still not 100% sure about what I’m doing. Any help would be very much appreciated.