Have you read the documentation on creating website templates? What I'd do is create an install totally new from what you have to do some testing to see what happens when you create a template, create a new site using the template and try to export a site. This will give you a better picture of what happens and what you can and can't or shouldn't include.
There are many ways to do this. For instance, I have a template that is setup to have all the settings configured the way I need/want, only includes minimal templates and layouts, has a default stylesheet (empty actually) and sets a master page with a template. I use this every time I start a new website. Pretty generic but saves me about 2 hours each time.
If you're creating sub sites, I'd imagine you'd want to include some page templates maybe a reference to a "global" type stylesheet that has the overall layout of the site (responsive, normalize, etc.) and maybe set some default settings.
To better understand what can and can't be included at the site level, take a look at your current site and see what Assigned Objects are already included or what you can exclude. If it's not in that list, then it's considered global.