I would use a 1-14 three groove Pac Nor or a 3 groove Lilja. I have found that the 3 groove barrels seem to copper foul less than the standard 5-6groove barrels.
I would for sure have zero freebore in the chamber so that I would get an extra 1000 rounds+ out of the barrel instead of the standard freebore. I would do a little research and see what is a loaded dia in the neck and order a reamer with .002 clearance over that dimension. I would also send the reamer maker(Pacific Precision) 5 peices of brass and have the reamer ground with a clearance of .002+ in the web area to completely eliminate any bulge in front of the web. I would also have a 1 1/2* leade angle ground on the reamer. The throat dia needs to be .2245.
What I am trying to say is that you can have a custom gun, but that chamber will give you may additional features such as more velocity, longer case life, more usable barrel life due to the short leade and perhaps better accuracy due to the bullet getting started straighter in the barrel due to reamer design.
Gunsmiths have to satisfy a variety of different customer needs, so they can not be expected to stock quality reamers like this. I have had sevaral custom gunsmiths lie their [beeep] off telling me that they had a reamer like this, when I had them cut me a neck checker prior to chambering with their reamer, they started back peddling.
Having your own reamer made is the very first step in having a custom gun built, you will never regret having your own reamer made.
Some gunsmiths will throat your chamber with the rounds seated at the seating depth with 3 dummy rounds that you provide to them...they are rare indeed. Pac Nor does this at no additional charge.
I would use a remington action due to the fact that the action can be trued.
Personally, I would not opt for shooting bullets heavier than 60g due to the terrible trajectory. If you do elect to shoot a 60g V Max, then the 1-*12 twist is needed.
If you want to shoot a heavy bullet in 22 caliber, then I would opt for a 22/6mm Remington which will shoot the 75'g V Max at 3800 with a 28" barrel, just don't expect long barrel life.
As for scope choice, I don't feel qualified to give you any advise since I do not know of what kind of hunting you intend to do.
One thought, the 22/250 Ackley Improved is slightly faster than the 220 Swift, you will never have to trim the brass to length. The OAL on the 22/250 is shorter than the swift, so you are intending to use the magazine and seat bullets to touch the lands, you are in a distinct advantage with the 22/250 AI.
With the last Custom 22/250 AI that I had, I had a 27" Stainless barrel with a reamer designed like I described above. I shot the 60's at 3700 fps, the 50's at 4200 fps, and the 55's at 4100 fps with amazing accuracy out of the 1-12 twist barrel using Win 760. The 22/250 AI is an amazingly accurate cartridge that requires minimal load development.
Best of luck to you!