If you've already got a .30-06, the .270 is not a must. Keep in mind, I'm not saying anything bad about the .270 here. It's a truly great cartridge. But, anything that you can do with the .270, you can already do with the .30-06. They're just too close that there's not a significant difference (except that the 06 is more versatile due to the ability to shoot bullets greater than 150 gr., so it'll work well on larger game where the .270 might be a bit marginal).

The .308 is also a virtual clone of the .30-06. But, if you consider the .308 to be a "dangerous game" cartridge, then you should consider the .30-06 to be in that category as well. The .308 is about 100 or so fps slower. It'll do just about anything the '06 will, and is available in a shorter action, which weighs in its favor if you hunt from a blind. All of the calibers we're talking about are available in semi-auto rifles. My first deer rifle was a Remington 742 in .30-06.

The .243 is an outstanding "tweener" cartridge between the .223 and the '06, particularly given the bullet sizes in your initial post.