If I can be allowed to throw in my 2 cents, I would suggest these two options. The 308 or the 300Win Mag. The 308 would be my first choice for a LR shooter. So much is known about this cartridge and there is so many components to load, that you really cant' go wrong.
I have shot my 308 to 1500yds and as long as I can judge the wind, I sure wouldn't want to be standing out there. There are shooters that go to 3000m with their 308. All you need is lots of elevation in your scope and mounts.
The 300 Win mag offers many of the 308's benefits and can be used, with the right bullets, for "longer" range hunting. The only downside is recoil, and barrel wear.
For an off the shelf rifle, I would look at the Savage models with the laminated and ventilated varmint/bench rest stock, heavy fluted stainless barrel. These rifles should shoot well enough to make 1000yds plinking a no brainer. The Savage short action tactical rifle is also an excellent choice. Best part is these rifles are very well priced and there is lots of support equipment for the Savages now.
The only thing you may have to add is a lighter aftermarket trigger. Slanted long range one piece bases are now available too.
With Fed Gold medal 308 brass, Lee Collet neck sizer, Varget powder and match primers, you should have no problems shooting sub MOA groups at long range using match bullets.
Welcome to this exciting and very fun part of shooting. Most of the bells and whistles you read about are great for those that have the experience. Start slow and burn lots of powder. By the time your barrel is cooked, you will have a very good idea of what you want and need. You may find that what you have is already more then you need.
Downsides for the Sako is poor stock design for bench shooting, higher price, and lack of scope mounting options. The varmint/tactical Remingtons, Winchesters, and Savages offer much more bang for the buck at this time.
Good luck...
Jerry