I think i can help here, hold on tight while i try to explain!
Firstly you would need some kind of set the amount of time for delivery depending on what they had selected. I assume it will be posted from the previous page so (you would need to set the value that it passed as a number for this to work, so 1 for next day and 3 for standard)...
$delivery_duration = $_POST['delivery_duration'];
$delivery_day = $POST['delivery_day'];
$delivery_month= $POST['delivery_month];
$delivery_year= $POST['delivery_year];
Then you need to work out the date, obviously this is a problem, you cant just add 3 or 1 because if its the end of the month or the year it will mess things up, what you need to do is convert it to days.
Now PHP can do this using the cal_to_jd function. It doesnt convert it to just a day of this year, but that doesnt matter because there's a function to convert it back so first convert it:
$deliv_in_days = cal_to_jd(CAL_GREGORIAN,$delivery_month,$delivery_year,$delivery_year);
Now you have the days in the julian day format so add the delivery time:
$dispatch_in_days = $deliv_in_days + $delivery_duration;
Then convert back, this returns an array:
$dispatch_date_array = cal_from_jd($dispate_in_days,CAL_GREGORIAN;
So then get your dispatch date from the array:
$dispatch = $dispatch_date_array[date];
Then you just need to save it into your db.
More info is available about the functions and how they work in the manual