how to match a sentence to a cluster of keywords?
I am kind of confused by the question. But I am guessing you are asking what model to use and how to represent words. 

This seems like a pretty introductory example so you may want to try simple Bag-of-words representation. Try pushing that into a Naive Bayes classifier as a first pass. If you are unhappy with the results, you can implement word2vec and more complex methods.