If you're going to build a segmented handle out of burl, you'll want to have it stabilized and then cored for your handle. Your cue maker will undoubtedly know what to do. Some nice burls that come to mind are amboyna, thuya, buckeye, afzelia, and madrone. I think leaving a little sapwood on the ends of amboyna makes a neat and unusual appearance. Buckeye burl can also be stunning.
Mr H