You can move the posts and all other data from the default WP db tables with the WP Export function and import them with the WordPress Importer plugin.
But before you import the data make sure that some of the db tables of the new blog are empty. You need to clear the wp_posts, wp_postmeta, wp_comments, wp_commentmeta, wp_terms, wp_term_taxonomy and wp_term_relationships table before you start the WordPress Importer and import the data from the .xml file. For instance if the Hello World post and the default category would remain in the db of the new blog the WordPress Importer would change the ID numbers of the imported posts, comments and categories. It would add the imported data to the existing data and would not replace existing elements with the same name automatically and because two things can't have the same ID, the Importer would change the IDs of the imported elements. But that would destroy for instance the relations between the posts and the statistic results.
If you would like to migrate existing statistic tables of podPress then you need to do this with a different plugin or directly through the web interface of your db server (e.g. phpMyAdmin etc.).
(I believe that you would need do this also for other non-default db tables (e.g. db tables of other plugins).)
Afterwards you can adjust the podPress settings of the new blog.
If you want to move the media files to a different location too then you would probably need to adjust the URLs in the podPress data. You may do this manually by opening each post in the editor again or you could use a little plugin. Please read more about this topic here: http://wordpress.org/support/topic/moved-podcasts-to-new-website-is-it-possible-to-update-all-paths
Maybe you try this procedure in a test environment. I use XAMPP to create and run a test blog on my local computer.
One further very important issue is the feed URL. If you have registered your feed e.g. at the iTunes podcast repository then you need to communicate the new URL to this server. The best way to do this is to run the old and the new blog at the same time for some days and to use the itunes:new-feed-url function in the old blog. If you activate this function and enter the new feed URL, podPress will add the regarding element to the old feed. The iTunes server will recognize the element and take over the new URL. Afterwards the iTunes server will retrieve the information from the new feed automatically. Once the iTunes server does that, you can retire the old blog.