There is no one best cartridge for wapiti.
I personally prefer a 338 WinMag. Have used a 375HH to good effect.
I wouldn' t recommend going below 30-06 power.
If you' ve hunted deer, just remember elk are not deer: triple weight double tough.
The cost between the same rifle in standard and magnum cartridges is seldom more than a couple hundred dollars.
If a couple hundred dollar difference in rifle cost is prohibitive then I recommend against wapiti hunting.
Even with resident licenses and six hour travel time it just is not a cheap thing to do.

Never Go Undergunned

EKM