Feature extraction for sound classification
By long shot it is doable - to what extend? You will see. This task of environmental sound classification is not very well studied. Also choice of machine learning paradigm is crucial - statistical approach or maybe binary classifier? You can start with GMM's, ANN's and SVM's - I opt for GMM's and ANN's.
Yes, most of people are using MFCC's because they are well correlated with what people are actually hearing and also no one came up with anything better since. You might also want to add extra features such as MPEG-7 descriptors.  Proper feature optimisation must be performed because sometimes you don't need so many features, especially when they are do not separable. For more info please refer to my previous answers:


Feature extraction from spectrum
MFCC extraction
Detection of sounds