I am going to suggest something out of the box that nobody else has yet.
While I am sure that a $1500 custom shop Savage is going to shoot lights out, I can't help but think that for what your goals are, you don't need to spend that much on a custom gun. If you were going to be using it in competition and really trying to wring the accuracy out of it, absolutely put up the cash and go for it.
Lets look at .25 compared to .5 moa at 1000 yards. .5 moa at 1000 yards is 5 inches, .25 is 2.5 inches. I don't think someone who is just having fun shooting a long ways is going to notice a .25 compared to a .5. Wind is going to have far more affect on long range shooting that .25moa accuracy. Most people who want to have long range fun shoot at 12x12 or larger steel plates so they get feedback and instant gratification.
But you are not going to be hand loading or shooting competitively. Shooting tiny groups is going to come with practice, you can't just buy a skill. You are looking at a minimum $100 to $180 max? in factory ammo for 100 shots. I don't know how many rounds it is going to take you to achieve the level of skill and consistency needed to make tiny groups, but 1000 rounds is going to be a big chunk of cash in itself.
What I would suggest is to get a savage/stevens 200 in 308($300), a pac-nor or similar prechambered barrel select match barrel, in either 6.5 creed or 308($450), aftermarket trigger or accutrigger ($100), and aftermarket stock($100-400) and a swfa fixed power scope 12 or 16 power ($300). Put it all together and bed the stock, if you feel capable or take it to a gunsmith and they will do it for much less than a remington. Then sell the take offs, the barrel alone will get 60-100 back.
The stock stevens action is more than capable of great accuracy
Shooting A 223 Rifle To A Mile Accurately
Any stock that is bedded, pillared, and free floated is going to work well enough and those things are pretty easy to do, but getting a stock that already has pillars simplifies the work a lot. Regardless of what stock you get you are going to have to bed it(they might have that done on a savage custom shop).
This is more than enough to shoot .5 moa out to 1000 and including optics, you spent a total of $1300(depending on stock and trigger) leaving you $1700 to spend on PRACTICE. you can knock 450 off by practicing with the stock 308 barrel and then replacing it when you wanna stretch out and need more accuracy. Even less if you find a used action.
For simply a range "fun" gun fixed power stevens action works and you get a sense of accomplishment and pride pulling it all together. If you don't end up liking the gun or long range shooting for that matter, all those parts will sell easily(try finding a stripped stevens action). A custom savage might not sell as quickly as that action is not as versatile.
Simply my opinion, obviously, but I am cheap and like to try a thing out and see if I actually have time and desire to actually do it before I spend $3000 on a gun and optics and potently another $1000 to $2000 on ammo.
Normally they do much better than that. 
