That list of three would work for me as well, two of three are favourites of mine. I would pass on the /06 however. For my uses I much prefer the .308Win. That said I too am a huge fan of the 6.5x55, brilliant, just brilliant round, two of the three other guys I deer hunt with on and off have Tikka T3s so chambered. I would happily wander bush with a .260Rem as well. The down side to me of the 6.5 is needing a long action to run it in. I prefer my general hunting rifles in the medium length action (and in particular the Sako AII). My 5x go to rifles are .22RF (mine is a Brno), .22/250 (factory Sako AII), .308Win (custom on a Sako AII action), .300Win (Weatherby) and .375H&H (Winchester M70).
About 5 years ago I settled on 5 rounds and built from there....22 LR, 5.56/223, 308, 9mm and 12 ga......they will do anything I need to do and since I reload they are even more versatile....all five can be subsonic and 4 can be loaded a million different ways....I have a 22 Suppressor and it's quieter than a pellet rifle, I also have a 5.56 Suppressor and with 69+ grain bullets it is as quiet as the rimfire subsonic and more deadly than you think....you could write a book on all the ways you can load a 308, from mice to elephants....
I do not live around nor do I care to shoot elephants or rhino or hippo or T Rex. If I have the opportunity I'd like to hunt brown bear in Alaska, and a few more of the north america game animals. That said the largest gun I own and expect to ever need for the big stuff is the Rossi lever gun .454 ,and as a side arm 45 long colt. The very smallest game being squirrel to critters up to 20 lbs. air guns in both .177 and .22 are quite adequate and not noisy enough to alert all the critters in a mile square area . As for medium game 20 lbs to 200 lbs .117 HMR , although 17 HMR is not legal for deer, I know those that have take deer with .17 HMR. The 17 hornet is more than capable, and is a center fire round. If it's accuracy is up with the 17 HMR the velocity is more than a match for much larger game . Bullet placement for a clean kill, will be the chief factor in all hunting experience regardless of rifle caliber .
the stick is just the minimum requirement for entry to the "he who shalt not be named" club. (Am I allowed to mess with him when he's no longer here?) To become an officer, you gotta be able to snare em with a thread.
I'd have to go with . 22 S L LR, in my dad's old Mossberg bolt rifle. .30-06 in my Custom Mauser sporter. 12ga in my Mossberg combo gun, 24" vent rib w/screw in chokes and a rifle sighted (smooth bore) 20" barrel. I'm a vet, and I would also need a fighting rifle. Now that I'm older and have some physical challenges, probably a 5.56N.