Don't overthink this one, looking for some angle to help your rankings. Google expects certain types of websites to regularly refresh their existing content and to add new URLs. Other types of sites would change existing pages and add new urls at a much slower pace. Both are signs of freshness - but just do it naturally for your specific type of site and its visitors.
No, the home page does not need to be dynamic for the site to be considered "fresh". But it might be good for your users if the Home Page shows a link to your recent posts. If you have backlinks to your Home Page, it could also speed up crawling and ranking for new articles, too.
[edited by: tedster at 8:27 pm (utc) on Nov. 26, 2007]