Given the choice between 270 or 308 I would recommend the 308 for some of the reason you enumerate. Since you want/need fast follow-ups, the short action has an advantage and it's lighter. The 308 will also provide you with better barrel life than the 270.
From your post it sounds as though you might have the 270win and a 280rem mixed up. The 270 is .277" or 6.8mm and the 280 is .284" or 7mm. Both are based on the 30-06 case, just necked down.
You're right, 7mm bullets offer excellent BCs and a 280Rem would be a great choice (I have one). My 280 - Updated!
As for shooting pigs and punching threw bones, that's less dependent on the cartridge and much more dependent on bullet construction. To do damage on less than perfectly placed shots on pigs, you want a tough bullet. So think Accubond, Barnes X, Sierra Match King etc.
As for rifle choice, here in the US a Rem700 SPS Varmint can be had fairly inexpensively ($450US). The barrel and action comes in flat black. The stock is plastic but replacement stocks for Rem700 are abundant and relatively inexpensive. My longrange/tactical rig started out as a Rem700SPS Varmint: My 308 1k Rifle - The Evolution Continues!
Be sure to read the thread all the way to the end and you will see the rifle transform into a full-custom.
As for optics, given your varied shooting from up-close to longrange, consider something with a magnification range of 4-14 or 5-20. As the magnification goes up, you need the 50mm front objective. Remember that exit pupil on a scope = diameter of objective divided by magnification. Optimum exit pupil size is 5mm.
As for specific optics, look at Bushnell, Nikon, Sightron, Leupold and if you've got the wallet for it, NightForce.