Copying Drupal to a webhosting service
Roughly speaking, the procedure is to


copy all files to your webserver
create a database on the webserver
export the local database
import the db export in the webserver db
edit settings.php and set the new db name, user and pass
enjoy


The recommended webserver specs can be found at http://drupal.org/requirements. Since you have been developing on Linux, Apache and MySQL, use the same on your webserver (unless there is an important reason to change it). Also pay attention to your PHP version. Recent Ubuntu versions come with PHP 5.3, so it's best to use that on your server as well.

To prevent problems while importing your database (especially if you're using a tool like phpMyAdmin), it can help to empty (truncate) all cache_ tables before exporting it.