Make sure to check the state regulations on caliber restrictions. The best caliber to hunt elk with, is almost always the caliber you shoot the most accurate with, and are the most comfortable with. A 338RUM is useless if one can not hit the broad side of a barn due to the fierce recoil. Depending on range, and terrain/vegetation, a 243 would suffice, though not my idea of a good gun. A 30/30 in the hands of a competent shooter can, and has killed its fair share of elk. You just have to accept your maximum distance limits. I myself, have a 30/30, 30'06, 7mm rem mag, 300 win mag, 300RUM, 375H&H, and a 45/70, and every one of them is suitable for elk, and I have plenty of trigger time behind them all, so I am confident with them. A 308, 270, 280, all your 30 caliber magnums, 7mm's, and pretty much on up from there works. If you want to shoot longer ranges, and are capable, then look at the 300 magnums and bigger.

My 7mm mag, and 300RUM are both winchester M70s, and have seen elk hunting. The 300win is an Xbolt, and is what my wife shoots, and the 375 is a remmy 798. If I'm going to hunt wide open area, or thinner timber, the RUM comes with me. If I dont know what I'll see, the 7mm or 375 comes with me, as they have lower power scopes. If its thick timber and brush, my marlin 45/70 with ghost ring sights rides alongside me.
Thats my two cents, not adjusted for inflation.