I have quite a few such drop-down menu lists on my various webpages.
You have a very good start but you can't make it work with just html. You need to write a program in javascript (not java which is an entirely differnt thing) to do it. (You could do it in java, but javascript is far easier.)
Here's a simple
page that has one. Look at the source and you'll see the javascript program in the head and also and "onchage="cd()" call to the program from within the option list.
You could pretty much cut and paste something like this, changing the function name and the variable names to suit you. Also, you will need to name your form as well as the option list.
W3Javascript school has a good introduction.
It seems complicated but it's pretty simple to just cut and paste it. I can send you a PM and be more specific if you want.