Use a custom logger

At the very least, call https://golang.org/pkg/log/#New from main and pass to the handler constructors. This way we can make our tests less noisy.

Maybe upgrade to https://godoc.org/github.com/golang/glog or https://github.com/op/go-logging or https://github.com/juju/loggo or something, though https://dave.cheney.net/2015/11/05/lets-talk-about-logging argues against it.

Start at main and trace the handler constructors to see how logging is currently wired. Use Go's log.New as described in the issue, pass the logger into the handlers, and verify that the tests are less noisy; optional logging-library upgrades are separate possibilities.

Written by the indexing model from the issue text.