Add mypy type annotations where appropriate

Now that we're on Python 3, we can use mypy and static type annotations to catch mistakes faster:

http://www.mypy-lang.org/
http://www.mypy-lang.org/examples.html

Start by reviewing the Python codebase and the mypy documentation linked in the issue, including its examples. Determine which modules and annotation scope are appropriate before making changes. Done should mean the agreed code has useful annotations and mypy runs successfully, but the issue does not define that scope or a test command.

Written by the indexing model from the issue text.