what are you comfortable shooting with?
I've talked with a Dad @ work who's twelve-year old took an Elk with a .243.
Can your shoulder stand the recoil of an 30-06 or above?
What caliber allows you keep all shots on a paper plate @ max range e.g.: 10, 150 or 200???
Jack O'Connor love and promoted the .270 Win, based on the 30-06 case,
look at the list from RCBS 30-06 leads the most popular caliber, meaning it will be readily available, 30/30 has been used on Elk but placement and range are critical.
The Swede's use the 6.5X55Mauser on Moose, again its placement.
Tell us more, so we can refine this.
PS, I use nothing but .308Win, not able to try Elk this year but will next.