Hindley-Milner is cool, but if you're planning on implementing a language with type inference, I strongly suggest you take inspiration from bidirectional type inference, notably Pierce-Turner[1] and subsequently Dunfield-Krishnaswami[2]. These algorithms are capable of inferring much more complex types and generally produce better error messages. Typically, there are very few programs which can't be typed when you combine Dunfield-Krishnaswami type inference and have the user place annotations on major function definitions.
[1] http://www.cis.upenn.edu/~bcpierce/papers/lti-toplas.pdf
[2] https://arxiv.org/pdf/1306.6032.pdf