Relative brightness of the sun's corona In preperation for the upcoming solar eclipse I'd like to practice my photography to be able to take some (hopefully) good photos of the corona during totallity.

What is the brightness of the sun's corona? How bright is it compared to a full moon (or other celestial phenomena)?

At what point during the "diamond ring" does it become too bright to look at safely without safety equipment, and what is the relative brightness of the diamond?
The corona varies dramatically in brightness from the inner portion near the sun to the outer portion a few solar radii away. The innermost portion is the brightest; at ISO 100 and f5.6, an exposure of ~1/125 second will capture it. So it's roughly the same brightness as the full moon. The outer corona will require much longer exposures of perhaps a half second, but note that during this time the sun will move noticeably with a long lens if you're not using a tracking mount, so some blurring will likely occur. Overall, practicing on the crescent moon will give you a pretty good idea of the dynamic range of the corona.

The diamond ring is dangerous to look at directly, as is any unobscured part of the sun's disk; you should look away at first glimpse, or earlier.

There's lots more detail scattered around the web, which you've probably found by now. A good overview is available at http://www.mreclipse.com/Totality2/TotalityCh12-3.html#SEExpoTab