Don't listen to the guy's building 600 yard and beyond guns if your talking 500 and in. Iwould never build a 26" barreled gun for hunting inside 500 yards.
The velocity gain is not worth the trade off for accuracy in a field gun, better ballance, and at least a pound in wieght!
I would stick to Standard Brass, skip the magnum. I built what I considered what you are, a one gun for any big game. I'm talking inside 400, to maybe 500 in the right sittuation, on anything from Antelope and Deer to Elk. But if it ever became a chance, have enough for Grizzlies, to Moose inside 200 to 300 on the long end.
I chose a 338/06, and 20 1/4" barrel. It gets just north of 3000fps with the 180's, over 2870 with 200 grain, and 270fps with 225 grain bullets. And all shoot to the same POI!
Those groups were all shot from a clean cold barrel, and all were 1" for 5 shots, the 180 grain bullet load was 3 and under 5/8". But those were just finishing up barrel break in, trying fifferent loads.
Those longer barrels will shoot as good, but not if you change powder and bullet weight like the shorter will. And yes it will do better with a worked up load, the 180 Accubond is the only one I have dialed in so far. Bottom right bull, 3 shots, clean cold barrel, and right at 3000fps @ 100 yards.
But then to prove it, i shot two seperate shots at 236 yards on a steel gong, both shots were from a clean cold barrel! After all that is what counts from a hunting rifle.
I have never built a big game rifle with a barrel under 22" most have been 24", and i have built a few, or I should say, had them built. But none of those other rifles would shoot as consitent as this, and none were as reliable with that first shot!
But if I was you, I would go with your first thought on the shorter barrel. And as far as cartridge, I couldn't be happier with the 338/06. But whatever caliber you choose, make sure you chose one that will give you 90%+ load density, with medium burning rate powders like, Varget or N140. You will be happy, I know I was!