Couldn't this be done using category, or a tags. I don't know enough php/html to write this but what if the values of the drop down is the same name as your categories.
Using php you could call the value selected in the drop down and assign it as a variable and then limit the posts on the page by that variable.
$CAT = the_dropdown_value;
// Get the ID of a given category
$category_id = get_cat_ID( $CAT );
while (have_posts()) : the_post();
As I said I am not a great coder as of yet so don't try this out. this post is to help agelonwl come up with a solution for you.