As a gunsmith I much prefer the Rem 700 over any other factory action to build extreme accuracy rifles on. They are simply as near to perfect as they come from the factory for blue-printing and accurizing into some scary accurate rifles.
That said, I have built on the Sako actions with good results.
Your question about best all around 30 caliber is a tricky one. It all depends on what you need this rifle to do anf how far you will be shooting and what you will be shooting at.
If your just punching paper at ranges out to 600 yards or so at the most, the 308 Win is pretty hard to beat. Of course out of a factory rifle, you will be stretching the capabilities of either a Rem or a Sako as they come out of the box, at least on average.
If you plan on shooting farther or hunting at longer ranges I would recommend something a little moer potent but that will not be an option in the style of rifle you are looking at at least not from the factory.
One idea would be a Rem M700 short action either rechambered, or preferably rebarreled with a quality barrel to something like the 300 WSM
in a match grade chamber and throat.
This little round is doing quite well for extreme range shooting when the rifle is designed for the VLD bullets or even the 200 and 220 gr Sierra MK's which are kind of a semi-VLD compared to others.
I do not recommend the 240 gr Mk in the 300 WSM unless you are using a 30" barrel. They can be used with fine results and may are doing so but I like 3000 fps at least from my extreme range rifles and out of a 26" WSM, this is not practical.
There are even those using fast twist 308 win's with the 240 gr pills but bullet drop is pretty severe and requires absolute scope adjustment and range measurement for good shot placement at ranges past 800 yards.
For punching paper this is fine but for game, I do not like the increased difficulty presented by the steeper bullet drop.
From there out You will need a full length action for real extreme range performance. Rounds like the 300 Win Mag, the 300 Jarrett, and the other full length standard belted magnums in 308 are great for 1000 yard shooting and even beyond.
Even the 30-378 and better yet the 30-378 Kahn with its conventional 35 degree shoulder are amazing extreme range hammers but at a cost of recoil and shorter barrel life.
If I had to pick one 308 for the best all around selection, it would probably be the 300 Win Mag.
It has plenty of case for bullets up to 240 gr out of a 28" barrel, brass is cheap and quality, does not need anything special in action lengths. Not so big that recoil is a problem and relatively easy on the throat and bore.
It is easily capable of shooting at closer ranges as well as at extreme ranges, again in a quality rifle, not a factory rifle on average.
So I guess it depends on your goals for the rifle. Once you define those, its much easier to select a round/rifle to meet those goals.