I'd like to be notified if a particular user contacts me for Chat.
Well, there is no such feature. Whatever feature is available on Google Talk is the same for all the users who can chat with you - no subdivisions, categorization, branching etc... The feature you are asking for is do available in many Cell Phones when it comes to Voice and Video Calls, but not in Google Talk, Facebook Chat, Yahoo Messenger etc...
But on Facebook you have the option to receive text messages on your mobile when a particular person/ group of persons specified by you send a message.