Which section to use depends on what look you are after. If you want the white smooth look, try to find a tine that is as close to your finished diameter as possible with as little curve as possible. If you are looking for more color and texture, try turning the main beams down to size. Be sure to seal with CA. If you want to leave a patch of bark on the finished pen, try a piece with a little more curve.
The best way to drill antler is to set the cut piece between centers and spin it at high speed. Look down at the piece and you will be able to see a shadow, which will be the largest diameter straight dowel you can get out of that piece. You can adjust the position of the centers to maximize this size. Then turn enough of the piece down to a cylinder to either grip in your scroll chuck to drill on the lathe, or with your vice to drill at a drill press. Center the drill bit on the impression from the live center and you should drill through the center of the blank.
Antler differs quite a bit depending on the variety of ungulate it is from. in general, the larger the antler the larger the spongy core is and the thinner the solid walls. As a general rule, the most dense and least spongy antlers are either sambar stag or axis deer, whitetail are somewhere in the middle but change greatly by age of critter and diet, ect. Elk and moose are generally too spongy to turn the main beams effectively down to pen size, but the tines and tips can be used.
These folks have a pretty consistent supply of axis antler on ebay, and while their posted prices are pretty high, I have called them and they are willing to work with people who are interested in Non-exhibition pieces, and for bulk prices much more reasonably.
www.thewildliferanch.com
Antler can be pretty effectively bleached using hydrogen peroxide, and can be dyed back to a natural tan to brown with a solution of potassium permangenate.