You can get the value of the field and set to a variable then verify the options. Here is the code:
<?php
$option = $the_field('myfield');
if($option == "1"){ $color = "red";}
elseif($option == "2"){ $color = "blue"; }
elseif($option == "3"){$color = "green"; }
?>
<div style="background-color: <?php echo $color; ?>; ">My Content</div>
Of course there is other ways to do it, like an array with the options and the colors etc.. but the ideia is the same.
Hope this helps you. =D