(1) "I am thinking through when to upgrade to a wordpress.org site."
There are no rules of thumb. IMHO if you intend to move to self-hosting there is no advantage to remaining at wordpress.COM, aside from learning how to use the software better as you have lost of peer support here on the forum that's lacking at wordpress.ORG.
Some bloggers start out on free hosted blog platforms like wordpress.com or blogspot (Blogger) on a test basis. They plan to establish traffic, purchase a domain and then to switch over to paid hosting.
The Technorati Authority and Rank as well as the Google Page Rank belong to the sub-domain url for your blog. If purchase a domain and move your blog on to it those will disappear unless you also purchase domain mapping.
(2) " really like the idea of the front page remaining the blog page where post are kept. Anyway, I guess what I am trying to say is that I am mapping out the content of site. What are the rules of thumb on when it is best have a static page, and when it is best to make new posts with specific categories?"
The front page remaining the blog posts where posts appear immediately after publication in reverse chronological order with the most recent on top is characteristic of blogs. You could say it's what a blog is all about as blogs are set up for the convenience of readers who come to read the most recent posts.
They only purpose having a static front page serves is to appease the aesthetic preference of the blogger, as opposed to the convenience of the readers. Establishing a static landing page as the front page means each time readers come to read posts they must endure the annoyance and inconvenience of clicking through it every time they wish to read posts. There is no benefit at all to the readers, thus choosing to do the same gives rise to the question: Who are you blogging for?
(3) " ... when it is best to make new posts with specific categories?"
Blogs are all about posts. Every post ought to be assigned to broad categories and should have specific tags. These categories and tags are "keywords" for retrieval purposes just as they would be if posts were books in libraries and categories and tags were subjects in a library catalog.
Potential readers use search engines and when posts are properly constructed and categories and tags are assigned to them, they are indexed by search engines and appear in the SERPS (search engine results pages). That means they can be readily located by targeted readers who click through to the posts in question. Posts have Google juice and achieve PageRank.
(4) "For example, monthly podcast will be a major feature of our site. Should episodes be archived via a post category or a static page? Or both?"
Posts assigned to your Monthly Podcasts category can be located in the Archives which can be displayed in a widget or static page - the choice is yours. "Monthly Podcast" is a category and the tags assigned to any podcast ought to narrow the subject matter down to a direct hit.
Example: Suppose I have a marine mammals of the world blog and I publish my monthly podcasts in posts. The broad categories would be "marine mammals," Monthly Podcasts" and the names of the oceans (Atlantic, Pacific, Arctic, Indian, Southern).
The tags would differentiate individual posts according to their specific subject matter. One might be tagged "dolphins" another may be tagged "sea lions", etc. The tags may also reflect the specific geographical area and/or other unique specific subject matter in the podcast posts.
Blog Post title: The Effects of Polar Bear Predation on Sea Lion Populations in Bering Strait.
Categories: Arctic Ocean, Marine Mammals, Monthly Podcasts
Tags: Bering Strait, feeding, predation, polar bears, sea lions, population