The PHP Manual notes:
mysql_pconnect() acts very much like mysql_connect() with two major differences.
First, when connecting, the function would first try to find a (persistent) link that's already open with the same host, username and password. If one is found, an identifier for it will be returned instead of opening a new connection.
Second, the connection to the SQL server will not be closed when the execution of the script ends. Instead, the link will remain open for future use (mysql_close() will not close links established by mysql_pconnect()).
...
Using persistent connections can require a bit of tuning of your Apache and MySQL configurations to ensure that you do not exceed the number of connections allowed by MySQL.
As for your "Connecting to the database - good or bad ways for speed?", I'm not very sure, 0.0013 probably isnt accurate, since there are many factors involved, and different queries should result in different timings.
From the looks of it, I would just stick to mysql_connect() unless you really have a design requirement to use persistent connections.
A possible modified version of your connecting/selecting script is:
<?php
//connect to database server
$dbcnx = @mysql_connect("XXX", "XX", "XXX")
OR exit("Unable to connect to the database server at this time.");
//select the jokes database
@mysql_select_db("newcentury21", $dbcnx)
OR exit("Unable to locate the database at this time.");
?>
of course you need only call it once per script, and mysql_close() usually is not needed.