Nothing smaller than 270 and preferably larger. Don't go out and buy a gun you are scared of. Shot placement is far much more important than caliber. We have found that the new controlled expansion bullets (like the jacketed hollow point) are no good. Plenty of penetration, but not enough expansion. On the other hand, the new ballistic tip bullets are worse. Too much expansion on the surface and zero penetration.
The absolute best bullet for elk is a partition bullet. Nosler partition bullets are what we recommend. Barnes bullets are also good. Upon arrival, a trip to the shooting range to check your gun is mandatory. Many things can happen to a gun during travel and it is only smart to check it out upon arrival.
The only shot we recommend on an elk is the bread basket, or engine room, if you please. Never shoot an elk in the neck or shoulder. There is so much meat in the neck that unless spined, the elk will most likely get away. There is so much bone as well as meat on the shoulder that this shot could just cripple the animal and it might escape. Shoot for the “tickle spot” (as our 12 year old niece would say), 1/3 of the way up the chest behind the shoulder.