As to type of action, I recommend a bolt-action Mauser type or any bolt-action rifle with controlled feed/claw type extractor : classic Winchester 70, Parker Hale, etc. It's good insurance against double feeding because a Mauser generally won't double feed. If you double feed when the boar is charging at you, you are screwed because once the gun double feeds it can take a long time to clear the malfunction.
As to caliber.... I'd use a 30-06 : bigger than a 270Win, very popular, won WWII, endless ammo choices(you can go into any gun store IN THE WORLD and the store would probably have it on the shelf), can be used as a deer caliber, medium recoil, good flat trajectory, good knockdown power, reasonably priced ammo.