This document is updated on the basis of feedback received.
You bought Ardour, but the free-from-source version comes with the Gentoo Studio installer. Before installing your paid version, simply run:
emerge -C ardour
Then install the paid version.
Browsers & Audio
Which browser should you use? Any browser you want. Any browser that handles sound at all should be usable via ALSA, but not all browsers have JACK support. Firefox supports JACK, but Firefox-bin does not.