A 300 Win Mag in a trued Mauser action, 1:8 twist #3 barrel 26", Maple stock glass bed, 6x42 scope New SWFA used Leupold.
A 338 Edge in a Howa Action, 1:9 twist #3 barrel, Walnut economy grade wood checkered heavily pillar bedded and glassed, Burris 4x12 scope
These would kill anything that walks and breaths in North America from Kodiac Bear to Deer. The top one could be used almost any place on earth. The bottom one is a Wildcat so that rules out most countries but would work just fine in North America.
To be honest though anything that shoots flatter than a 45-70 that can push big heavy bullets would work. 35 Wheelen, 30-06, 7mm Rem Mag, 338 Win Mag, 8mm Mauser, 270, 7mm Mauser, 6.5x57 RWS think Mauser. If you rule out Kodiac Bear and Moose you can even include things like 260 Remington, 25-06 etc.....
Truth be told you could drop anything in North America with a $50 Mauser you bought from a gas station in 8mm Mauser with the rifles sitting in a barrel. 500m is not hard to do even with iron sights. Keep in mind your shooting large game usually with their head down eating grass when you shoot. That does not require 1/4 MOA rifle! Shooting sticks super handy! I load my 8x57 Mauser with 196-200gr bullets. If I hit it it goes down.
Practicing freq. to keep your shooting skills sharp and having good field craft are what you really need more than any amount of gear. Being able to accurately range and read the wind again is more important than the cartridge. Knowing how to stalk an animal is super useful if you are going to be shooting 500m and under. The closer you can get the less likely you are to mis-read range or wind!