I would suggest you rethink the GUI.
There is no combo list box for browsers, but there should be.
What you could do, to help your users and save yourself a lot of dev time is use a cookie.
Set a cookie with the last few values that a user types into a text box and display them in a "separate" drop down box called "History", for instance.
The nice thing about php and cookies is that you can call them just like variables during the page load.
As far as autocomplete goes, you are looking at a pretty hefty algorithm. Basically you would have a database that contains all of the possible words that could be typed. After the user types the first letter, you would capture it and query for all of the words that start with that letter. Then you capture the second and query for words that begin with those two letters and so on... It is a drill-down tree model.
Once you have a sufficient number of letters typed, you can begin filling in the textbox.
Agreed, this is not something that is best attempted on a scripting level, but is better when compiled into more efficient code.
--brian