I think i will put in for an idaho sheep tag just for the fact its a luck of the draw state and ive also thought about new mexico elk for the same reason.
I'd recommend saving your money on Idaho sheep unless you plan to use the hunting license to hunt OTC deer or something like that. Very few people truly understand how poor the odds really are in that state due to the non-resident cap. Your odds of drawing a random sheep tag in Wyoming are as good or better in many units. My wife and I apply heavily for sheep, and I've probably only applied in Idaho 2 or 3 times in the past 30 years, and I went into it knowing my odds were poor.
You live in what is the best antelope state, and certainly one of the top elk states. Statistically you can draw units every three to four years that rival some of the best elk hunting available anywhere. Region G deer hunting now rivals some of the best hunts you would ever draw out of state, and you can do that every year. If it were me I would use your vacation time learn your own state well, few states can compete. Maybe even buy some stock and learn to hunt the backcountry, or backpack and use a packer.
For out of state, definitely buy deer points in Colorado.
If I were you, a young guy living in Wyoming with great hunting opportunities, rather than apply out of state, I would save my money for a hunt up north (Canada or Alaska) or some quality landowner tags down the road.
Just my thoughts.