Buckthorn is one of my favorite woods to work with. It is excellent in both tension and compression. Just be sure you cut it in winter when the sap is down as it is one of the most difficult woods to dry without it checking the heck out of its back. I would debark it, thin it down to just above bow dementions and then seal the back with lacquer or shellac. The sapwood dirrectly under the bark becomes the bows back, no chasing a ring necessary. Also, when you go to cut it, check for the flat side to the trunk, that will tell you if it is twisted or not.
As far as cross section goes, I would opt for a flatter belly and slightly crowned back for your first.
Like I said, it is near the top of my list as far as bow woods go, you wont be disappointed!!
Just out of curiosity, where do you live?
-Cody