I have owned 5 Tikka T3's: 270 WSM, 7mm RM, (2) 300 WSM. My current rifle is a 6.5 PRC (rebarreled the 270 WSM). I love their smooth actions and the ability to buy pre-fit, shoulder (fixed) replacement barrels. All the factory Tikkas shot in the .75 to 1.25 MOA range. Good enough for what you want to do. I would go with a used Sightron SIII 6-24x50 scope. Great glass. Repeatable turret dials. They can be found used for roughly $500 - $550.
As others have suggested, trigger time with your rifle/scope will be more important than what equipment or caliber you choose.
You haven't mentioned what expectations you have regarding trophy quality. If any old bull scoring 280-320 will do, then pick whatever equipment you like and practice. If your sights are set on a true trophy that could very well be a once in a life time experience, then make sure you have enough gun. The 6.5 PRC is a great caliber. It will kill elk 95% of the time, but the other 5% may be what you run into on your hunt.
Let's say you want to hold out for a true trophy bull in the 340-360 range. You find him in your pre-season scouting. You hunt hard for 5-7 days, passing up lesser bulls trying to hold out for your giant. On the final day of the hunt, bad weather moves in. Lots of fog and wind with this ice storm. The sun is going down as you come over a rise and catch your bull going up the hill on the opposite side of the valley at 680 yards. He stops and turns to look at his back trail, offering you a hard quartering away shot at his vitals. You have spent a lot of trigger time with you rifle and are confident you can make that shot. At that moment in time what caliber do you want in your hands?
This scenario may not ever happen top you and the 6.5 PRC will serve you well. But my luck seems to trend to the above example. If this is a once in a life time hunt and you want a true trophy - then I would leave nothing to chance. I would go with one of the bigger 7mm's, and most likely a 30 cal rifle. BTW - The larger magnums will thump you good in those light Tikka rifles.