As an alternative to Hindley-Milner, also consider a compositional type system (https://unsafePerform.IO/projects/talks/2016-06-compty/CompT... it should be a very good match for the kind of simple HM type systems that you're going to encounter while learning about compilers.

Here's code if you prefer that to slides: https://github.com/gergoerdi/hm-compo