Problem: I would like to know how to best export and import Toolset information across sites.

Solution: In general, you should use the built-in Toolset > Export / Import features for exporting and importing the following Toolset structures:
- Custom post types definitions
- Custom taxonomies definitions
- Custom field groups definitions
- Post relationship definitions
- Views
- Content Templates
- WordPress Archives
- Toolset Layouts
- Post Forms
- User Forms
- Relationship Forms
- WooCommerce Blocks settings
- Access settings

You should use the export tool built into WordPress (wp-admin > Tools > Export) to export your site content, for example:
- Posts, Pages, posts in Custom Post Types
-- The taxonomy terms associated with each post
-- The custom field values associated with each post
-- The post relationships associated with each post
- Media library items

Then use the import tool built into WordPress (wp-admin > Tools > Import) to import that site content, but only after you have imported the Toolset structures listed above.