WordPress has an Export/Import function you can use to backup and restore posts and categories. I hope that WordPress has this feature in its wp-admin section. Export the .xml file from the old site and import that .xml into the new site.
The other option would be to duplicate the database and point the new WordPress at that database and hope it can handle the upgrade of the database. WordPress updates the database during version upgrades, but I'm not sure how well WP3 will convert WP1 data.
If you're really daring, you can just point the new WordPress at your current database and see if it'll import. If that fails, you can use the DreamHost panel to restore your database.
WordPress database settings are stored in its config.php file.