joed, look into the 6.5 Creedmore or some other cartridge created for bench rest shooting. Here is a website loaded full of information for you to do research.
http://www.6mmbr.com/index.html
If you roll your own then you have a plethora of calibers that are not the norm for you to build on, and will give you better results for what you are wanting to accomplish. I think you owe it to yourself to open up your options, and IMO will be pleased with what you find. As mentioned the .25-06 and .22-250 are great hunting cartridges, and are very accurate. But not really marketed as bench rest calibers.
I have seen many shooting in "F" class using the 6XC, and the groups at 600 meters look like a .50 cal hole. It is a funky looking cartridges, but they shoot long and really buck the wind. I have seen people shoot them at 1000 meters, and it is amazing at the accuracy they get.
Have you looked into the Tubb 2000 space guns? These guns are capable of being adjusted to fit you to the 'T'. Meaning your arm reach, your check height, etc. allowing you to have the exact same hold each shot.
http://www.davidtubb.com/tubb-2000-spec-tac-lr-rifles
Yeah... The gun is very expensive, but can be built on a budget build for half the cost.
A good bolt gun in the BR calibers should give you the results you so desire also. If you are building the rifle for "long" range shooting a Savage action with a custom barrel, a good stock with proper bedding in a BR caliber is a good choice, and would probably be the way I'd go instead of a Tubb 2000 because you could have a superb rifle for around $1800 to $2000 after the bedding, trigger and glass.
The 6XC is built on the .22-250 case.
http://www.6mmbr.com/6XC.html
Here is a picture of the round.
I am not trying to say the two choices you have mentioned are not good rounds, but giving you some research to do, and steering you towards better suited calibers and chamberings for you to accomplish your goals. I am not a BR shooter, but by shooting HP competition I have seen some of these type rifles shooting off the line, and they are amazing. Truly amazing at the accuracy they give. Even in heavy crosswinds. Leave your options open until you do some more research.
You will not be off in cost although I do not know what your budget is, but by getting into the 'real' long range calibers and guns you could be saving yourself some headaches, and save some money in the long run.