To train a neural network, you must have a large amount of data to get good results. If you have just 60 samples and cannot get more, I highly suggest you use Transfer learning.
You aren't going to get an absolute answer. Larger is obviously better, but it should not take a lot of work to do a train/test split and try training, see how accurate you get. The real answer is that it depends on how accurate you need this to be.