If you havnt bought a rifle yet you can think about doing this in stages to save some cash.
There is a huge aftermarket for Savage and Remington and with the internet order stuff isnt too hard to get. You could get a Savage 10 FCP which comes with a McMillan or HS Precision stock;(about $1100-1300) Remington which comes with a Bell and Carlson. Savage also has the BA and there is the Remington 700 P. There are probably more threads on this forum about Savage vs Remington then anyone can count, I have both and they can both shoot about the same; just which one you like better and what you want. Check out all of them is what I would suggest.
Get a decent scope,($900 for Sightron, $1300 Leupold, $1800+ Nightforce) bed the action (prices vary you can do it yourself, or pay about $150) start shooting. Get more money get some reloading stuff. Keep shooting. Get more money swap the barrel for a Shilen, Kreiger etc. Keep shooting. Swap out trigger for a timmney or jewel or whatever you want. Continue on with this until your rifle is the way you want it. This isnt exactly out of the box but this process will get the job done. .308 will also run you quite a bit less the then .338 LM.
This will still be cheaper then a Sako and definitely cheaper then a Coyote. If on the other hand you have a surplus of money then spend it up Sako and PGW are awesome, buy a Timberwolf if you have the cash, the only reason I dont have one of each is because I cant afford to...yet.