Going back to the OP, he already has and shoots a 25-06. This is a lovely fast and flat shoot calibre ideal for longer range work on smaller animals, but will quite happily deal with large Red Stags.
30-06 and also the 7x64 or 280 Remington would be a perfect compliment giving you a rifle that would provide more authority on bigger tougher animals eg big Red Deer, Boar, African plains game etc but still plenty flat enough shooting for any mountain hunting with the correct bullet and load.
An argument could be made for stepping up to a 300 Magnum of some description. These add perhaps another 50m of point blank range and a bit more power but at expense of a lot more powder, recoil noise etc. and for longer range these point blank is much less of an issue, as range finders and good trajectory info takes the guesswork away. Wind is always and always will be an issue. Even long high BC bullets are blown around in the wind.
The beauty of the 30-06 is that it is a worldwide calibre and hunting ammo is pretty much available in most places.
Personally I really like the 7x64 and 7x65r just because, but a 30-06 is probably the more useful and easier to run choice.
A lot of the myths about 270s, 30-06 etc come from shooters who are new to rifle shooting and / have never been taught how to control recoil. Everyone seems to use the tactical crossarmed hold with the weight of the rifle taken on a bipod or bag, and then the free hand holds the butt into the shoulder. This works fine on a light recoiling rifle, especially one that has a thick heavy barrel. If you use a bipod on a heavy recoiling rifle and use you forehand as god intended to hold the forend, you hand just gets bitten by the bipod. Harris Bipods in particular seem to be designed to inflict as much damage as possible. Ditch the bipod, take a good grasp of the forend and rest your hand on a bag, on sticks etc and your forearm acts as a big recoil spring and takes a lot of sting out of any recoil. And this technique gives more consistency in recoiling sporting rifles across a whole range of shooting positions. Also wood, and wood laminate stocks soak up and don’t resonate recoil like many plastic / polymer type stocks.
). I find it more of a firm push than my 308 (sako 591) which is more snappy. It’s very manageable, I really don’t think ‘ought six’ recoil is a factor unless the user is very recoil shy. Yes you lose sight picture, but you do with 308 and likely much above 243 depending on the rifle weight/loading etc. 
the 300 win mag was exceptionally tempting and who knows one day I may opt for one but for everything I want...it’s too much !
