Modify PHP to Return Data from External Db

I built a website sometime ago which uses a drop down search to create a table – see here My Old Website

I am now trying to replicate this is wordpress. But can’t get my head around how to bring this into WordPress. I’m pretty sure how to connect to my external Db using `
$mydb= new wpdb(‘DbUser’,’PW’,’DBName’,’localhost’);` but no idea how to have a combo box and select query on submit (or change)

How do I something this simple in WordPress. My PHP code from website is below. Really appreciate any advice you have.

<form method="post" action="Dukes3Availability.php">
<input type="hidden" name="submitted" value="true"/>

<label>Search Month to See Availability Details and Prices:

<select name="Category" id="Catergory">

<option>Please Choose Month</option>
<option>February 2014</option>
<option>March 2014</option>
<option>April 2014</option>
<option>May 2014</option>
<option>June 2014</option>
<option>July 2014</option>
<option>August 2014</option>
<option>September 2014</option>
<option>October 2014</option>
<option>November 2014</option>
<option>December 2014</option>
<option>January 2015</option>
</select>
</label>
<input type="submit"/>
</form>

<?php

if (isset($_POST['submitted'])) {

include('Connection.php');

$Category = $_POST['Category'];
$criteria= $_POST['criteria'];
$query = "select Date_Format(Start_Date,'%d-%b-%Y') As Start_Date,Day,No_Of_Nights,CONCAT('£', FORMAT(cost, 2)) as Cost ,Status,PageLink from <code>web152-thenorth</code>.Dukes3 WHERE concatc = '$Category' ORDER BY Start_Date";
$result = mysqli_query($dbcon, $query) or die($query);
echo "<table>";
echo "<tr>
<th>
Arrival
</th>
<th>
Arr Day
</th>
<th>
No Nights
</th>
<th>
Cost
</th>
<th>
Status
</th>
<th>
Link
</th>
</tr>";

while ($row = mysqli_fetch_array($result, MYSQLI_ASSOC)) {

echo "<tr><td>";
echo $row['Start_Date'];
echo "</td><td>";
echo $row['Day'];
echo "</td><td>";
echo $row['No_Of_Nights'];
echo "</td><td>";
echo $row['Cost'];
echo "</td><td>";
echo $row['Status'];
echo "</td><td>";
echo $row['PageLink'];
echo "</td></tr>";
}

echo "</table>";

} // end of If Statement

?>

Thank you.

theNORTH