Switch from TSLint to typescript-eslint

This repository still uses TSLint, which is being deprecated: https://github.com/palantir/tslint/issues/4534. It'd be great to move it over to [typescript-eslint](http://typescript-eslint.io) to no longer use deprecated packages.

Protip: [tslint-to-eslint-config](https://github.com/typescript-eslint/tslint-to-eslint-config) is the recommended package to do so!