question of select data from database to be a opition

None of what you have said indicates a need to use AJAX, so don't use it.

1. Don't use AJAX unless you need to.
2. No one should be using the old MySQL connection any longer. Use PDO or MySQLi.
3. You really need to use stripslashes and htmlspecialchars on the staff id field? Isn't it just an integer?
4. In the non-database example you use an id and name, but in your database example you pull just the id.
5. The for loop is not the efficient way to do this. Use a while loop

Here is a complete PDO example.

<?php

// PDO connection - it goes in a separate file, as you did for your mySQL connection

// Note that you need to replace the variables with your own

$dsn ='mysql:dbname=xxx;host=localhost;port=3306';
$user='xxx';
$password='xxx';
try {
$dbh = new PDO($dsn, $user, $password, array(PDO::MYSQL_ATTR_INIT_COMMAND => "SET NAMES utf8"));
//$dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_SILENT);
$dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION); // change to SILENT for production

}
catch (PDOException $e) {
     die('Connection failed: ');
}

//  end of connection script to put in separate file

if ($_POST){

echo "<pre>";

print_r($_POST);

echo "</pre>";

}

// now we get the data -- correct the variable names first or it will now work

$sql = $dbh->prepare("
SELECT        staffid, staff_lastname
FROM             staff
ORDER BY staff_lastname");
try {
$sql->execute()or $response = "<h3>Request  Failed.</h3>";
}catch(PDOException $e)
{    echo $e;}  
if ($response){
echo $response;
}
while($result = $sql->fetch(PDO::FETCH_ASSOC)){
$staff_optionset.= "<option value='".$result['staffid']."'>".$result['staff_lastname']."</option>";
}

// so now you have the options in one chuck which you can place within the select tags using PHP

?>

<form action='' method='post'>

<select name="users" >

<?php echo $staff_optionset ; ?>

  </select>

<input type='submit' value='submit'/>

</form>