When you have a WordPress site, you will notice that there are both Categories and Tags. We will assume that the Categories will be for your new articles/postings assigned to their proper category section.
A typical website structure can consist of a Homepage, Products/Services, Resources, About and Contact just to name a few. From there you may have a blog section for posting news/articles. This is typically used for your Postings assigned under Categories.
Set Categories to follow and index as normal. These pages will receive PageRank/Link Juice. And for that reason, you do not want to have duplicate categories.. This just dilutes the keyword targeting for the top keywords on the website. Targeting the same keyword on multiple pages within the website can actually work against your own rankings.
Set your Tags to noindex/noarchive. This is so no PageRank/Link Juice will be passed on the tag section pages. Tags are helpful to further connect related articles. The tags section of the website should just be for users to help navigate through the site, and not for keyword targeting.
The homepage, and main topic sections on your homepage will be the main areas that will be targeting your top keywords, and your articles/news postings within the Categories will be receiving PageRank/Link Juice, so these will help with driving additional traffic to your website.
Also depending on your site structure and size, you may also want to block some/all categories and let the post keep some PageRank. In a case like this you could have the main news page keep PR and then if you have the posts also sectioned off into a topic specific category, these could be set to Noindex.
Every site will differ depending on overall site structure and your goals.