Add a better API for managing the client's connection state

[jneem]

The protocol is stateful. From the client's end, you

• send a request
• get back the stderr message stream
• if there wasn't an error, get the response

Our client supports all these steps, but it isn't easy to figure out how to put them together. Also, there's some unnecessary boilerplate involved in dealing with the stderr messages. We can keep the API that we have right now, but we should also add a friendlier and more discoverable layer on top. See also #9