Sheep draws are kind of a personal issue.
Each persons situation is different.
Some states require that you pay the entire tag fee upfront. Wyoming, Colorado. Then you are reimbursed if you do not draw.
Some states like Arizona, Idaho, Utah, Nevada, Oregon, require that you purchase a non refundable hunting license.
New mexico requires that you buy a license, and pay the entire tag fee up front, but they refund the tag, plus the license if you don't draw.
So, it kind of depends on what your budget allows.
Plus, where you are interested in hunting.
There can be a big difference in tag price as well. Nevada tags for non residents are really reasonably priced compared to the other states.
The New mexico tag is expensive. Over $3,000.00!
Some states have really high numbers of applicants in the draw.
Others have surprisingly low numbers in the draws.
Way too complicated to go off a list if you ask me.
I don't want to draw a 50% success rate unit that typically harvests below average rams, just because a list shows it is better draw odds, or some other factor.
I spent 5 hours yesterday researching units in one state.
Where to put my son in, what rams they harvest, comparing to other units.
It takes countless hours to do for multiple states.
Oh, and if it only takes you 10 years to draw Colorado, please send me the list you use.
My recommendation to you is apply in as many as you can reasonably manage.
One option for you is to maximize your spending.
If you decide to apply in Idaho, apply for multi species. Since you are going to get stuck with owning a hunting license, you might as well put in for controlled hunts for deer, elk, ect. Plus, buy an over the counter deer tag, get out there and use it.
Unless you are the type who has money to blow on purchasing licenses that never get used.
Non resident hunting can get spendy. You gotta maximize.
Thats the beauty of the pay up front states. You have to have the cash to do it, but you get it all back if you don't draw.
The states with the buy a license and keep it, even if you don't draw, have to be done more carefully.
Its all about your personal situation, what you can afford, how many options you have.