Hi Jason
Glad you are liking the community so far! I would recommend starting with this post I did for Moz to help answer exactly these questions about WordPress and SEO: http://moz.com/blog/setup-wordpress-for-seo-success
When you're starting out and have just a few tags (6 isn't much) it's not a huge deal, but for some sites as they grow it turns into 300+ tags without planning on it - then it's a little more of an issue. Not something that would cause a penalty per se, but just not great for the site to have those extra pages indexed and existing because they don't generally add any value (they are often similar to the posts themselves).
I would use maybe 3-4 tags tops for any blog post. They are little detailed words to describe the content. Additionally, tags only have a utility if used as navigation in the site somehow: either a list of popular tags in the sidebar or sometimes you can click on the tags for each post at the bottom of the post.
Lots of people try to make tags to rank in search engines but I have found this to be a bad strategy. In general, I recommend people to noindex tags as shown in the article. With the Yoast SEO plugin for WordPress you should also "noindex subpages of archives".
Categories - I would create 5-7 categories that you will file all blog posts into - and only use those and don't let categories grow (don't keep adding new categories). You can customize your category pages with this plugin: http://wordpress.org/plugins/wp-custom-category-pages/ - and indexing them is fine.
Good luck!
-Dan
