Timberflint,
Over the last 35 years, I have used a variety of .224 centrefires including 222Rem, 22/250, 22/250 AI, 220 Swift, 220 Swift AI, 22/284, and 224 Clark (22/257 Roberts imp.). I believe the comments and suggestions by Fifty Driver, Crispin Goodall, and Brianb are excellent.
Although my best long range field shooting was done with a custom 22/250 (1 in 14 twist) some 35 years ago, I agree with Fifty Driver that the 22/250 AI, is probably the best option for the type of shooting you have in mind.
A 1 in 9 twist would be required to stabilise
a 75 grain VLD or the 75 grain Amax. A 1 in 8 twist would be required to stabilise the 80 grain VLD's of Berger and JLK. A 1 in 7 twist would be needed if you wanted to use the 90 grain JLK.
You may be tempted into using a larger capacity case to obtain the extra performance, but the trade off is that you require a quality SS barrel, and then contend with more frequent barrel cleaning to prevent fouling problems. The cases of 55+ grains capacity are hot after 3 shots in 3 minutes, so you have to space your shots if you want to avoid damage to the sensitive throat area.
However, if you can manage the problems, the performance from larger cases such as the 22/6m AI, which Fifty Driver mentioned is exhillerating, and I believe that he was being conservative when he mentioned the 400 fps differential between the larger cases and the 22/250.
To illustrate this, my .224 Clark achieved 3,930 fps with the 69 grain Sierra HPBT, and after 1600 shots I had the barrel set back and rechambered to the 22/250 AI, and in the same barrel with the same bullet, I am now getting 3,430 fps, which is a difference of 500 fps. Compared to the standard 22/250 it would be about 650 - 700 fps.
The case capacity of the 22/250 is about 43.0 grains, 22/250 AI 28 deg.- 49.2 grains, 220 Swift- 50.4 grains, 220 Swift AI 40 degree- 55.4 grains, 22/257 Roberts (22/6mm similar) - 57.1 grains, 22/284 - 63.8 grains, 224 Clark 63.8 grains. I understand that the newly introduced .223 WSSM has a capacity of about 54.5 grains, but the case requires that you use a different or modified boltface.
Good luck, and hope the above helps. Regards, Brian.