Original answer:
NNs can require a lot of data to train. For smaller datasets, knn or svm can be a better choice especially if the classification boundary does not need to be very complex or classes are tightly clustered within-class and far away from other classes. Also keep in mind the bayes error of your problem which is the best value you would be able to get over the set you want to generalize to with any classifier and is based on the separability and measurement noise in your data.