Tikka T-3, 308.
Modern 308 cartridges significantly out perform 30-06 from just a few years ago. Getting 2900 fps with 150's isn't hard and 3000 fps with longish barrels and handloads isn't impossible. For comparison the WW1 30-06 era loads were 2700 fps, by the 1940's it was only 2800 fps. Those were the numbers Townsend Whelen was looking at. Modern 30-06 loads are better still, but only beat 308 by about 100 fps. And the 30-06's reputation was built on loads that were less potent than todays 308.
Anything 30-06 does with bullets lighter than 200 gr 308 does as well with better accuracy and noticeably less recoil. If you need 200-230 gr bullets a 308 won't shoot them fast enough to be beneficial and 30-06 wins.
And don't get me wrong, I LIKE 30-06 and consider it the cartridge all others are judged against. It's just that the tiny gains in performance don't outweigh the 308's accuracy and recoil advantages.
The 270 is a great, classic hunting round and I understand why it has a following. It does what it was designed to do very well, but modern bullets, powder, and optics have negated its advantages. It was designed around shooting 130 gr bullets fast and flat. With todays optics a flat trajectory is far less important and heavier, more aerodynamic bullets perform better at longer ranges. Unfortunately 270 rifles aren't designed to use modern bullets. It was more by accident than design, but 30-06 and 308 will.
Another thing to consider is the future of the cartridges, 30-06 and 270 have been the standard for a long time, but both are in the twilight of their careers. It is getting harder to find new rifles in either chambering. Many new models aren't even being offered in either cartridge anymore.
That is my choice among your options. But a good argument can be made for 7-08 and 6.5 Creedmoor as well.