Welcome aboard! .303, of course! Just kidding but I'd wager that more moose have been killed in Newfoundland with a .303 than any other calibre. My father bought the sporterized version in the early fifties for $23. The full-stock model was $17. I was about 13 or 14 when I fired dad's .303 for the first time and I had no problem with the recoil.
I have a Remington 700 BDL in .270. The recoil was pretty mild but I put a Remington recoil pad on the rifle and that made it even nicer to shoot. I've recently been bitten "lightly" by the precision shooting bug with a view to shooting out to 1000 metres. So now I'm thinking about getting a .308. To my mind, the recoil from a .308 is slightly less than that of a .270 and an all-around great calibre to my mind. But that's just my opinion. And the .308 is fine for the moose and caribou on the island says this fellow Newfie.