Port codebase to TypeScript

[broofa]

Yet another issue for adding TS support to the project. This time, however, we'll (hopefully) be doing a full port of the codebase to TS so we can use tsc to generate the type declaration files.

This will affect the build system, which may (read, "definitely") break backward compatibility.

See PR #763 for specific tasks.

[broofa]

For the record, motivations here include:

• TS code is generally higher quality than vanilla JS
• Generating types automatically produces higher-quality type declarations and removes risk of errors
• Publishing types via the DefinitelyTyped project is relatively onerous and time consuming. Witness [@types/uuid]: Update for uuid v10 DefinitelyTyped/DefinitelyTyped#69773.