I went with a 308 for my first hunting rifle. I wanted readily available ammo (in case somehow I ran out on a trip or forgot it or something. I didnt want to be searching for 6.5-06 ammo at the feed store in Ballinger, TX.) I wanted something big enough for almost any game in NA, but not overkill for whitetail, which will be 95% of what I hunt. I didnt want a concussion from shooting.
IMO, 243, 308, 7mm Mag, 30-06, 270 would be good options. From there it is personal preference. I think the 308, day in day out, will will be more accurate than the others given availability of handloading and factory options.