Build String Based On Several Drop Downs

I'm trying to build a string based on three drop downs. As each drop down choice is made, I want to append the string and redisplay it. When finished the string will be a complete (but not hyperlinked) URL.

My drop downs look like this:

HTML Code:

PHP Code:

Here's how it supposed to work...

When an admin has used the first drop down to pick the value of the "first" variable, the string is updated and redisplayed like so:

Next, when an admin has used the second drop down to pick the value of the "second" variable, the string is updated and redisplayed like so:

Finally, when an admin has used the third drop down to pick the value of the "third" variable, the string is updated and redisplayed like so:

That's all I have. I'm stuck. I'm guessing I need an "onChange" event with each drop down? Also, I need to refresh the "makeTheLink" div when an onChange event fires? How do you tie all of this together? Is self rolled JavaScript the best solution or would jQuery be better?