Its funny that you ask...because I recently switched to a new cue...just a couple of months ago.
I very proudly play with a Morris Custom Cue made by Ned Morris of Desert Hot Springs, CA. Ned makes beautiful cues that are perfectly balanced...and he is a very responsive cuemaker (meaning that he will stick to his deadlines...and truly listen and understand what you are asking for). Predator Products provided a couple of unfinished shafts, and Ned matched them to a beautiful cue that he designed specifically for me.
Honestly, I cannot answer your question about the taper...because I don't know the answer myself. I have always just picked up cues to play with them...and if I like the way they feel or hit, then I keep them. (Ned's daughter, Melissa Morris, is a good friend of mine, and I once played with her and appreciated the way her cue felt. When the time came for me to get a new cue, I went straight to Ned first because I knew I wanted him to make it for me). But I do know that it weighs 19 oz. and there is a medium-hard tip on it (I think Le-Pro...I don't have to know exactly what kind because Ned kindly provided me with extras in case my tip goes bad). My break cue and my case were also provided to me by Predator Products.
I have always believed in supporting local cuemakers, and I used to play with a Pruitt (made by Ed Pruitt of Santa Monica, CA.
Melissa