With respect to big game cartridges, as long as you choose one with a bore size of 6.5 or greater you don't need to be concerned with which cartridge it is. All modern high velocity cartridges are extremely versatile when handloaded. So be more concerned about the rifle you choose and less concerned about the cartridge it is chambered for. You might find a rifle you like that isn't chambered for any of the cartridges you've mentioned, that doesn't make it a poor choice. If the rifle is capable of doing everything you require of it, and if you are competent with it, all is good. You should be concerned about the handiness of the rifle, the quality of the action and trigger, the ease by which you can mount the sights that are most appropriate to your needs, the stock material, and the LOP. Choose a bullet that is suitable for the job at hand and the cartridge, whatever it is, will do its part.