Switched hosts to one with cPanel. To transfer my blog should I do the WP install or just be uploading my old WP directory & database?

You can try the manual transfer, first copy all your tables on your new database. Then you need to update the wp-config.php file in order for it to be able to connect. In case you have the rewriting enabled, you may also need to update the htaccess file (if the rewritebase is different, it’s not that likely but it may happen).

Also check the chmod of your folders/files, there is an article about that.