I have to echo that the type of hunt you want will determine all your options and where you end up going. Mule deer in the west live in very diverse country and depending on time etc. things can be very different.
That being said, if you are thinking WY start buying point now and expect the price of the tag to jump $200 between now and then. I have been hunting in WY and am looking to add MT to my list here pretty soon. My hunts have ranged from timberline in early October, to desert in September to 2 foot snow November. Really not sure why you would not include CO in your list but I would look at it as well. Do you want a back pack hunt? A hunt from a central location accessible by truck? Do you want to hunt early high, late low? Hit the rut? Do you want to see lots of deer and a lower chance of a big one. Or see fewer deer knowing that you have a better chance at finding an older age class of buck?
Over all it really depends on what you want. For a good general hunt I like the look of teh MT set up as you can hunt later then in general than you can in other western states...
Gear will all depend on what you decide for the hunt..,