Go back and look for the stump. Thats where the best figured wood will be. These guys know their stuff. The branch crotches are the next most desirable pieces. The trees don't really have to be as large as mentioned above but they do need to be tight grained for quality dense blanks. There are several ways to stop the ends from checking, paint is OK, tar is better.
In the old days, boards were slowly cured for several years, some more than 20 years for highly figured wood, which is most likely to warp as well. Your drying procedure is extremely important. I know a furniture maker that likes to cut his own logs when he can get them. He will take hours on each log to figure out the best way to cut it to bring out the figure and avoid warpage and checking.
There is a lot more to this than is first apparent. If you have a lot of sap wood on the logs it may not be worh it at all. The last thing you want in any stock is "center ring wood". Any stock carved around it will never be stable.