My take - Get in New Mexico for sure. Idaho is a long way off and very rough. Apply there if you think you can handle it. Those 2 are both randoms, you don't have to worry about adding a point system. Then add 1-2 states a year. You can get overwhelmed if you try to do all of them at once. Add WY, CO, for sure then look at AZ, UT and NV and MT.
Do you guys bowhunt? This shortens the tag curve dramatically in a lot of areas, lower harvest success rates in general but at least you are out in the mountains learning how to hunt.