Takman, It looks like you are not interested in paying a fortune if you don't have to. For the money the 338 RUM is the best elk cartridge available. Accuracy velocity wise the 338 RUM, 338-300 ultramag or some on here call edge, and 338 lapua are virtually all the same. You or the elk would never know the difference with any of them. All are equally extremely accurate. Either will match any shot or video the other will do. The shooter and individual rifle are the difference. The main difference is you can buy a remington 700 338 RUM and bullets cheaper than the others.
I have all of these rifles and have taken elk at long distances with all of them. My Rem 700 338 RUM is factory except for bedding, trigger and muzzle brake
. It will easily take elk at 1000 yards. My load is 99 grains of RE 25 and a 225 nosler accubond at 3260 fps.
The 300 wby and ultramag will do the job but the big bore 338 is better. Since your starting from scratch may as well get the best. You can get a used 338-378 wby accumark for around $1000-1250 dollars like new from cabelas website. It already has a muzzle brake and gets you well beyond the ultramags and lapua. With 128 grains of H-870 I am shooting the 225 accubond 3540 fps with a 28" barrel extremely accurate out of my 338-378 wby. But all are accurate. Just pick the performance you want. You do not have to spend a fortune to shoot elk at long range. Just remember that with a custom rifle
the odds are better of getting a real shooter but no guarantee. You must way the price difference.