They will all do the job with the right shot placement, and a decent bullet. The ones you mention are good choices. I will be taking the 30-06 out tommorow, but have taken them with a 7.62x54R Sako M39, and 308Win, and even the 243 will do a fine job with a good shot. From 223-where legal...to 45-70, they all will do it, just depends on the amount of killing you want to inflict.
Personally I like the .30cals, but that's just my personal preferance.
243, 357, 30-30, 44Mag, 7.62x39, 7mm-08, 25-06, 270, 280, 308, 30-06, all of these are good cartridges in their own right.
Take your pic :toast:
-Aaron