RE: Montana
Most of the sheep units have large amounts of public land. Also, Montana is known for 180+ potential on thier sheep. They are not known so much for thier goats, although there are some units with better billies if you hunt hard. Look in the BC record book for Booner goats, and you will find some better states/provinces to put in.
The unlimited areas are tough, as has been noted, but there is a possibility of taking a sheep. However, I agree with the advise not to put in for them. The skivy is that if you draw an unlimited tag and don't fill it, you can keep applying for them the next year and so on. If you draw a limited area, you can't put in for 7 years (so you had better give it your best shot).
I have a friend who used to put in for an unlimited area that no longer is offered. He spent years figuring out (mostly on foot) where to find the best sheep(or sheep period). He finally found a great spot, but there were already tons of dudes hunting it. The hunters in unlimited units basically stake out the sheep prior to season, kill in the first couple of days, and then the unit closes due to the quotas being filled. The sheep in these units are not generally known for their size, although (like anywhere else), it is possible to find what you are looking for.
Put in for your points, if you spend the money and the time applying in a number of states, you will draw a tag. Hopefully you will still be young enough to scale the mountains.
Wyoming has a different system, where the people with the most preference points are alloted a better percentage chance for the majority of the tags. I.e. if you have 10 pts. you are basically guaranteed a tag in a number of units. You can apply for points only in July (100.00 ea. for bighorn), and when you get close, apply for the tag. However, in Wyoming you have to have an outfitter if you are hunting wilderness.
I posted a question wondering if anyone is a member of the Huntin' Fool, but it hasn't been answered, so I can only assume not many members of this site are. Check it out. It lays out 11 western states, draw odds on all species, when to apply, etc.... There are quite a number of sheep op's. out there.