Query clean up

I am looking for a clever developer to optimization for an online form for a website being developed. [login to view URL] Currently when a user enters a character into the field, the website would query the entire database (in order to show a dropdown box with relevant results and the user can click this for speed) and this is very slow, for example if there are 10 characters already, adding an 11th character would trigger a query to the server. Because long strings of text are expected to be in this field, it becomes very slow and inefficient for the user. We would like to solve this problem by using a wordpress plugin or writing some simple code in order cache that information so that the search results in the dropdown box that appear to do faster. This is an easily solved problem which I am expecting to take 1-3 hours. I do not mind how you solve this problem, if you should accept this project and find an already existing plugin which does it in 5 minutes this would be fine too. Thank you