I want to echo Alibiiv's remarks regarding caliber. I really don't think that 30-06 is the best choice for your stated goal. Don't take our word for it, do the math on your own. Do a comparison of a few different calibers for their efficiency. Look at the powder charge versus the velocity achieved. Look at the recoil energy generated for the terminal energy that you need at 4-500 yards. This will give you some scale of the 'efficiency' of the cartridge. My approach changed a few years ago. I now build rifles to shoot them 12 months out of the year, and I adapt them to the 1 or 2 shots per year that I take on hunting trips. That approach may not fit you, but you need hundreds of rounds of practice with shooting, and wind calls, and such to even take the 4-500 yard shot, in my opinion. 260 Rem, 7mm-08, and 6.5CM, and 308 Win seem to all be better choices, my opinion.
As far as brand.....I have a bunch of Remingtons, and I love them. But, I could not recommend them right now. The last couple that I had trued were way out in left field from being true. You will absolutely have to replace the trigger in the Remmy. So, whatever the cost of the rifle, you need to factor in $150-300 for a new trigger. I really don't think that there are any quality issues with a Tikka. Even their entry level, plastic stock is better than most. If you go that route, you can fill the butt stock with Lead BBs or some other media like that, and cut the recoil down while practicing. The actions are smooth, the triggers are excellent, right out of the box, and the price point excellent on them. I also would not overlook the savage, They just flat-out shoot. Get one one of the calibers above, with an accustock, accutrigger, and go to town. If and when you want to change calibers, or you shoot the barrel out, you can change the barrel yourself with minimal investment. I would recommend a model 10, or 12 over the model 11, for what that is worth. Keep us posted on what you decide.