Handling data imbalance and class number for classification
People talk a lot about data imbalance, but in general I think you don't need to worry about it unless your data is really imbalanced (like &lt;1% of one label).  50/200 is fine. If you build a logistic regression model on that dataset, the model will be biased towards the majority class - but if you gave me no information about an input to classify, the prior probability is that the new input is a member of the majority class anyway. 

The question you want to be able to answer is whether you are differentiating classes fine - so if you do have a minority class, do NOT use 'accuracy' as a metric. Use something like area under the ROC curve (commonly called AUC) instead.

If your data is really super imbalanced, you can either over-sample the minority class or use something called 'SMOTE', for "Synthetic Minority Over-Sampling Technique", which is a more advanced version of the same thing.  Some algorithms also let you set higher weights on minority classes, which essentially incentivizes the model to pay attention to the minority class by making minority-class errors cost more.

To learn to differentiate between lots of classes, I think (a) you will need to have a ton of examples to learn from and (b) a model that's expressive enough to capture class differences (like deep neural network, or boosted decision tree), and (c) use softmax output. If those still don't work, you might try a 'model-free' approach like K-nearest-neighbors, which matches each input to the most similar labeled data.  For kNN to work however, you need to have a very reasonable distance metric.