If you want to go elk HUNTING pick a spot and go for it. Lots of opportunity around if you are willing to work for it and can handle normal public land issues (other guys, inconsistent game, limited roads, etc.).

If you are set on elk KILLING pay the money and get a private land outfitter.

No wrong choice, just depends on what you want.

Don't get hung up on statistics. I know tons of guys here in Montana that would be counted in the harvest statistic but never actually make it out more then an afternoon or two. A lot of local "hunting" involves driving up somewhere, sitting for a while, getting cold, then heading to the bar to bitch about wolves killing all the elk.