I have a 243AI and love it, a little more velocity is a great thing, when you want it, and the case life is much better than a standard 243.
What size projectiles, any interest in suppressing: answering these will help. A 1:7.5 will stabilize at least 105s if not 115s. My gun loves the 105 Bergers. When I can find some 105 Amax, I'll run those if the gun likes them.
For hunting, there are many really good bullets out there. I prefer Barnes TSX or TTSX, but it all depends on what the gun likes.
Barrel taper depends on many things, you need to be very specific about what is most important and what is not.