Let me start by saying that I spend a lot more time on ballistics than I do on hunting. So this is more what the pencil and paper numbers indicate than something based on vast experience:

I think a lot of guys get into trouble with the 243 by using lighter bullets at high velocity. If a garden variety bullet impacts at more than 2800 FPS, the penetration will be less than it would at lower speed. More speed = less penetration. With a premium bullet, the story is a little different.

So if you pick the 243, I'd say go for as heavy a premium bullet as you can manage, and load it for perhaps 2750 FPS. Personally, I favor the Partition or the AccuBond. If you avoid a strike on a major bone, you'll get about a 16" wound channel and a dead moose/elk/deer. So I'm not opposed to a 243 with the right load.

All that said, I love my 6.5x55s and that would be my first choice. 140 grains of garden variety bullet at 2700 FPS is going to be pretty mild and very effective.

Be not weary in well doing.