I'm currently using neural network for classification of a dataset. Of course before doing classification either the data points or the features should be normalized. The toolbox which I'm using for neural network requires all values to be in range [0,1].
Does it make sense to first apply z-score (zero mean and unit standard deviation) and then to scale to range [0,1]?
Second, should I normalize along the feature vectors or the data points (either applying z-score or to range [0,1])?
You certainly need to normalize, however, some of these questions will depend on your application.
First: Scaling does not change the result of the z-score, since it is designed to be in terms of the standard deviation. However you will need to renormalize after the z-score if you decide to use it, to get within the range of [0,1].
Second: I don't understand the distinction between normalizing the features vs. the data points. Your choice of basis is depends on you. Whatever the points of data are that you plan to feed into your algorithm, those need to be normalized to [0,1]. How you want get them into that range depends heavily on your context.