I would stick with a caliber you can get anywhere like the 270,30/06,308
something that every Mom and Pop store would have on hand as you didn't mention about handloading. The rifle brand is up to you what feels good when you bring it up length of pull and buy the best scope you can as you never want to skimp on your optics especially if you want to shoot long range. I would stay with the Remington 700, Savage or a Ruger.
I have delt with the Tikka T3 line as I bought one for my girlfriend in 7mm-08 and it "DOESN'T" shoot any type of factory ammo in the guaranteed 1" moa! with that being said good luck to you in your quest.
Remember one thing on your long shots is you must follow up on everyone of them even if you think you know where your shot went as some times the animals don't act like anything has been done and they could be laying just out of sight from where you shot at them.