So you’ve decided to make your site responsive.
There are a ton of frameworks out there that can help you with this, I recommend Twitter Bootstrap, because well, its from Twitter and easy to get working. No other convincing to happen here. Good luck with your choice
jQuery-UI AutoComplete isn’t really compatible with Bootstrap. You can make it but there is a better way.
The answer to that is Twitter Typeahead which is really 2 different libraries that work together to make a very robust and well formatted system. How to implement Typeahead