Questions about companies in NM, MT, WY and CA
Let me answer your questions per state:
1) New Mexico - a curious state from company registration point of view. It is famous for its LLC (but not corporation), for number of reasons: as an out-of-stater you get an LLC that has no annual report, cheap to register (currently $50 if no expedited), and you enjoy the special provisions in New Mexico law making it a very good entity to use from anonymity point of view. NM LLC is a favorite tool of asset protection specialists.
Keep in mind though, many states do not require owners or officers to be listed, for example Wyoming and Delaware are same from that perspective. Still, some aspects of New Mexico LLC make it a good choice for specific uses.
2) Montana - frankly speaking, I am not intimately familiar with the special aspects of registering your vehicle under a Montana LLC, but I do know some people do that. Here is an interesting article I found online that you might want to take a look at to understand this question better: http://www.americas-mailbox.com/home/tips/montana-vehicle-registration.
3) If you plan to physically run your business from California it might be a good idea to register it as California LLC or corporation. You could still register it as Wyoming LLC or corporation, but since it has strong nexus in California you would still be forced to register it in California as foreign entity. California is probably the most aggressive state in that regard, so I would recommend you to take into consideration the fact that your business would have to be registered in California this way or another.