I don't think there is such a thing as an "ultimate" in anything. Your final selection will be a compromise based upon your priorities and resources.
Having said that I just resist the urge to share my 2 cents.
Long range shooting with a .224 caliber is problematic unless you are an expert at reading wind sign. .224 bullets will always suffer in wind due to their sectional density. Why build a custom weapon that is fundamentally flawed when you could select a 6-6.5mm bullet and greatly minimize your drift.
Overbore cartridges are not nearly as flexible as smaller cartridges when you are trying to work up a load. Your gonna find fewer good powder alternatives and you will spend more time tweaking the load for best accuracy. And overbore cartridges erode barrels quicker. For example, a barrel for a 6/284 may only last 1000 rounds. And it could take you 200 rounds to get your load right. Leaving you with 800 rounds of accurate shooting through your barrel.
Cartridges with low pressure limits also make it more difficult to work up that magic load. A lot of the Ackley Improved cartridges have lower pressure limits than the standard cartridges they derive from. This makes it more difficult to realize the benefits of the increased powder capacity if you are going to stay within the limits.
Long range shooting takes practice so choose a firearm that you can afford to practice with.
I wouldn't get too enamored with a high muzzle velocity. For long range shooting the speed retained down range is where you start seeing the benefits of a flat trajectory and less wind drift. To do this you will need to select a bullet with a high ballistic coefficient. The 6.5mm and 7mm bullets tend to have the highest ballistic coefficents.
So weighed against some of the things I've pointed out here. I would select a cartridge of at least 6mm with excellent bullet selection. A cartridge that was not overbore. Preferrably a cartridge that was on the efficient side. A cartridge that had demonstrable accuracy. A cartridge that had a large amount of info available for accurate loads. A cartridge that wouldn't burn out barrels too quickly. I would want at least 2-3 thousand accurate rounds out of a barrel. I would want a cartridge with higher pressure limits. Not that I would actually push it that hard but I want more flexibility in load selection.
Here are the cartridges that meet the criteria.
6mm BRX
- IMR 4895 34.8gr 3288fps 56875psi, 87gr Hornady V-MAX .4 bc
6mm Dasher
- IMR 4895 34.1gr 3267fps 56875psi, 87gr Hornady V-MAX .4 bc
6mm XC Tubbs
- H4350 44.2gr 3395fps 56875psi, 87gr Hornady V-MAX .4 bc
6-6.5x47 Lapua
- H4350 41.4gr 3272fps 53820psi, 87gr Hornady V-MAX .4 bc
6.5x47 Lapua
- IMR 4895 37.9gr 3078fps 55205psi, 108gr Lapua Scenar .478 bc
This info came from quickload.
All of these are used in bench rest competition. The 1000yd Camp Perry competition has been won with the 6xc Tubbs. All the cartridges listed are rated between 63000 and 65000 psi so the sample loads I've shown are not overly agressive. The 6.5x47 Lapua is a commercial cartridge. Factory ammo is available as is factory brass.