Use Babel to transform JSX instead of TypeScript

[toolness]

This is another attempt to set up our build pipeline so we can try out lingui, or any of the other i10n libraries that use babel plugins to transform/collect strings in JSX. See #488 for rationale on why this needs to be done.

Instead of migrating away from ts-jest like the previous attempt (#492) tried to do, this PR attempts to fix ts-jest via kulshekhar/ts-jest#1004.

Notes

• I tried disabling type checking in ts-jest to see if tests would run faster, but they didn't, which was surprising, since it vastly speeds up our webpack side of things. Odd.

• This moves our build and test TypeScript compiler options to a new tsconfig.build.json file.

To do

• Remove the --no-cache from the test:watch target.
• See if we can actually set "jsx": "react" in tsconfig.json so that we get lint errors when we don't import React for anything with JSX in it, but change it to preserve in our actual build pipeline.