Boogieman,
I shoot every weekend with three buddies and we, like you, are into accurate rifles but don't have the budgets to splurge on custom stuff. I thought that you might want some data on several different manufacturers to help your decision. I gave measured all my groups since I started hand loading so I can hopefully provide a reasonable comparison of the relative accuracy of the different rifles.
I have two Savages, both Model 10 Law Enforcement models in .308, a Remington 700 in .22-250 and a CZs .223. All are bolt actions and have Varmint or bull barrels and are my range rifles. I also have a CZ .30-06 and Winchester Model 70 in .270 with a hunting barrel.
I bought my first Savage about 7 years ago, an old Model 10 FP with a blind magazine. It shot so well out of the box that after seeing my results shooting a lot of factory ammo and hand loads, all three of my buddies and my son bought one, in .308 and .223, and two of them bought both calibers.
I learned to reload with that old Savage and tried all kinds of bullets and powders. I eventually shot 6300 hand load rounds through that old 10 FP Savage as well as a batch of factory match ammo and eventually eroded the chamber enough that I was having to seat the bullets out so far that I wasn't able to maintain constant neck tension because there wasn't enough bullet in the neck. Out of the box it averaged 0.623 but its top 25 hand loads averaged 0.446 at 100 yards. I tried a lot of strange combinations and some pretty lousy hand loads when I was learning.
When the old Savage accuracy started to deteriorate, I bought another Savage 10 FCP-K with a muzzle brake and it shot better that the old FP out of the box. But in all honesty, I concentrated on using the loads that I found worked well with the old 10 FP and probably skewed the comparison a lot.
I finally sent the 10 FP back to Savage and had them rebarrel it with a target barrel in .308. It took 30 days and only cost $ 427 including shipping. The new barrel shoots better than all of them. It's overall average for 741 hand load groups is 0.389 at 100 yards. The top 25 hand loads average 0.248.
The Savage 10 FCP-K with the muzzle brake is the second best shooter with an overall average of 0.447 for 718 hand load groups at 100 yards. The top 25 hand loads average 0.264.
While I was shooting the Savages, I bought a Remington 700 SPS in .22-250 at a really great sale. It was OK but needed a Timney trigger and a new B&C Medalist stock to make is shoot as accurately as I would like. Its average is 0.461 at 100 yards for 1296 groups. It has a 1:14 twist and shoots 40 and 52 grain bullets really well but accuracy starts to fall off at 55 grains and heavier. It is my third best shooter now, but it couldn't do that out of the box with the bad factory trigger and the Tupperware stock that came with it.
The CZ .223 Varmint shoots as good as the Remington with an average of 0.463 but was and still is out of the box. I have also shot from 35 grain to 73 grain hand loads in a 1:9 twist so the overall average is a bit misleading because that barrel doesn't maintain its accuracy with bullets heavier than 63 grains. I pushed the twist a bit more than I should have during my experimentation.
Both the Rem 700 and the CZ .223 have identical top 25 hand load averages of 0.212 inches at 100 yards so I consider them equally accurate with their favorite loads.
My buddies and my son now own 7 Savages and they are all good shooters and all still in out of the box configurations. They also own 3 CZs and they are also good shooters out of the box.
The only rifle that I had to change triggers and stocks on to get accuracy was the Remington 700. The barreled action on the Remington is great, but the trigger and the stock on the SPS couldn't deliver the accuracy that the barreled action was capable of. Fortunately, starting with the bargain buy, after adding the replacement trigger and stock the price of the 700 was just about the same as the Savages so the results worked out about the same.
You are right to opt for a Varmint or bull barrel for a range rifle. My hunting rifles, the CZ .30-06 and the Model 70 .270 have hunting barrels and they are great for one and sometimes two rounds and then the barrels start to heat up and the next rounds open up the group and I have to let the barrels cool down to get back to POA. They are made for cold barrel shooting.
At the range, I like to shoot at least a group while I am behind the scope.
All of our range rifles have high power scopes so we can aim small at 100 yards. I would recommend that if you want to get the most accuracy out of your rifle. We like to try to make the POA exactly the same for every shot when we are trying for accuracy. We use thin reticles do they don't block the aim point. We are very competitive with each other and measure groups with On Target and share the data on all our loads.
I've tried scopes at 15X, 24X and even 30X and 36X with the range rifles. One of my buddies even has a 45X fixed power Leupold scope on one of his Savages. The 24X and above scopes got better results than the 15X, so over the years I have managed to get all of my best rifles equipped with scopes of 32X and above. I have found that reasonably priced Sightron 36X fixed power scopes with 1/8 MOA target dot reticles are very effective. I splurged on a NightForce 8-32x56mm Benchrest scope that is now mounted on my 10 FXP-K Savage. It was on a closeout sale and it is a beautiful scope but I can't afford to buy another one.
Good luck on you search for your accurate rifle out of the box. My searches have been fun.