No, a column data type of "text" will work with your code.
Can you try the code I posted and tell me if you get an error message? Does print($c_id) display anything in your browser? If yes, then make sure you have values in the "countries_name" column of your table.
If nothing is being displayed (and in lieu of you describing what you are seeing so far), my next guess is that you are not connecting with your database via a link resource. You need something like this:
$result = mysql_query("SELECT countries_id, countries_name FROM countries", $db_conn)
or die(mysql_error());