I turn 95% dry wood. I don't like waiting for a bowl to dry so I can turn it again. I have a moisture meter I got at Woodcraft (on sale) and here in west TX, I'm usually looking for 6-10% moisture level.
I picked up some a downed tree at my late grandfather's place to make some bowls for a silent auction for a family reunion. When I cut it up for bowl blanks, I tested each piece of dry wood to make sure it would stand up to turning. I cut away any obviously punky wood. If I could dig it out in chunks with my fingernails or pocket knife, it got cut away. Loose bark was knocked off before I put it on the lathe. I turn found wood with a faceplate to start and in this case I used 2.5" wood screws to make sure I had a good hold on it. The bowls were going to be deep, so that wasn't a problem.
Watch out for weak spots like bark inclusions, knots, and insect damage. Some insect tracks can be used for aesthetic value, but some just looks dirty. Just have to see how you feel about it.
Don't forget to cut out the pith. That's where most cracks start.