Migrating to WordPress – but how will it do “structured” data?

Structured, as you named it, data in WordPress is combination of following features:

• [custom] post type – more accurately described as content type, you can register custom instead of bending generic “post” post type;
• taxonomies – for organizing posts into groups (native “category” and “tag” are taxonomies);
• custom fields – for storing bits of data with posts.

After you determine how you requirements are best mapped to these you will need to:

1. Register CPTs / Taxonomies.
2. Come up with appropriate interface for them in admin (scale is wide from basic native bits to very elaborate and specialized interfaces there).
3. Implement display of these in theme.