I am using php/mysql to create a login system. I have the following users table

CREATE TABLE `users` (
`id` smallint unsigned NOT NULL auto_increment,
`username` varchar(100) NOT NULL default '',
`password` varchar(100) NOT NULL,
`session_id` varchar( 32 ) NULL,
`email` varchar(75) NOT NULL default '',
`regdate` date NOT NULL,
`regip` varchar(30) NOT NULL default '',
`active` tinyint NOT NULL,
`isAdmin` tinyint NOT NULL default '0',
UNIQUE (`email`),
PRIMARY KEY (`id`)
);

to hold the data of each registered user (who fills out)
http://fixmysite.us/masterasp/register.php
Once the form is filled out, the database is updated. I want a welcome message so the user is welcomed by name once they are logged in, This is t he code I have so far, but I dont know how to retrieve the username
PHP Code:
<?php
// Run a quick check to see if we are an authenticated user or not  
// First, we set a 'is the user logged in' flag to false by default.  
$isUserLoggedIn false;  
$session session_id();
$query "SELECT * FROM users WHERE session_id = '".$session."' LIMIT 1";  
$userResult mysql_query($query) or die ("Error in query: $query. ".mysql_error()); 
if(
mysql_num_rows($userResult) == 1){  
    
$_SESSION['user'] = mysql_fetch_assoc($userResult);  
    
$isUserLoggedIn true;
    echo 
"Welcome";
    echo 
"<ul>";
    echo 
"<li><a href=\"/masterasp/logout.php\">Logout</a></li>";
    echo 
"</ul>";
} else {  
    echo 
"<ul>";
    echo 
"<li><a href=\"/masterasp/login.php\">Login</a></li>";
    echo 
"<li><a href=\"/masterasp/register.php\">Register</a></li>";
    echo 
"</ul>";
}
?>