The way the tag system works for non-residents is you have to put in for your tag first. Everybody that put in for the deer-elk non-resident combination license (tag) in 2011 drew, and the excess were sold on a first-come, first-served basis. However, this is not a gaurantee that 2012 will go the same way. Still, your odds are pretty darn good. They give less deer-only combination licenses, and I don't know the odds.
Once you draw your deer or deer/elk combination license (also known as "general license"), you can put in for limited entry permits. Most of the limited entry permits are on the Western side of the state. You can hunt most of the state with your general tag, especially the Eastern side. If you just want to hunt the Eastern side, like most non-residents, you won't need a special deer permit in most areas. In most areas your general tag is good for any either sex (buck or doe), either species (mule or whitetail). The district-by-district regulations on the MT FWP website spells out the "General Deer" regulations for each area. If the regulations say "Mule deer hunting by permit only" you would need to draw the permit for that unit to hunt mule deer there.
I would recommend applying as a party. The whole party goes in as one. If you are drawn, everybody gets the license or permit, if not, nobody does.
I would recommend getting the "Block Management" information for the Eastern regions (regions 4,5,6,7) and figuring out where to go from there. Block Management areas are private lands that are open to the public. You provide the Block Management area manager with your license number, they get a check from the state, and you get to hunt at no additional cost. There are great hunting opportunities in some Block Management areas.
Start doing some research, and I would be glad to help with some more info after you narrow down where you will be heading.