The easiest kind of hunting is pronghorn antelope in Wyoming - and Wyoming has some inexpensive non resident tags. Basically, hunting pronghorn in Wyoming is like going out to a drive-by shooting only in the plains ...

Next easiest would be deer hunting. I'd look through the Division's data for success ratios for GMU's and look for several GMU with a good success ratio, and then narrow down to GMU's with plenty of public land. Go do some deer hunting before trying for elk would be my suggestion. Elk hunting is harder hunting in some ways. Its hard to describe the differences between deer and elk hunting really, it sort of has to be experienced.

In the meantime, go do a lot of walking in the wild and practice observing game in the field so that you can learn to spot game. Novices often miss game because they've not trained themselves to observe.