Post Types
I would certainly register ‘News’, ‘Events’ and ‘Opportunities’ as custom post types, while maybe keeping ‘Articles’ as the default ‘Post’ post type. (See the Codex on custom post types).
This would, among other things, allow you to register/de-register metaboxes for specific post types where appropriate. Also, as requested, ‘News’, ‘Events’, etc will have their own menu tab (like Posts, Pages, Links etc.).
This would help with the second request…
Custom Taxonomies
To each post type you can register a custom taxonomy (see Codex on custom taxonomy). They come in two types: hierarchical (like categories) and non-hierarchical (like tags). (See register_taxonomy)
This would allow you to create ‘news categories’, etc. This will only be visible on the post types you register them for, (that is the meta-box will only appear on those post types). So the news categories would only appear on the news post type.
A final note, if you want ‘global’ tags (that appear on each post type) you just need to give each of your custom post types the ability to support the ‘tags’ taxonomy when you register them (see the taxonomies argument register_post_type).