RE: 7mm-08 or 280 Rem
As suggested when you flip that coin you should know that if it lands on edge it means you must get a 7MM Mauser.
The 280 Remington (along with the 30-06) is among a select few cartridges that can adequately handle all the worlds big game from pronghorns to eland with a light weight rifle. DG excepted of course.
The advantage of a short action is slight to nonexistant IMO but the advantage of being capable of driving a 175 grain bullet at very respectable speeds falls in favor of the 280 remington.
In 1903 when the 30-03 was developed for the military, had they opted for the .284 diameter instead of the .308 diameter bullet there would not be any where near the number of 30-06 rifles in the world. There would be no need for them at all. The .28-06 would be the world's leading cartridge. Today we call it the 280 Remington.