First, what fish will you target? Being in Wyoming, a good assumption is trout, but maybe you're after Northerns? Bass? Panfish?
Secondly, where will you be fishing - tiny streams, big rivers, ponds or lakes? All of the above?
Third, what's your budget? If you plan on wading, do you already have waders/boots?
Talk to local resources, whether they be a fly shop, or a fly club. Failing that, there are a number of forums that are more specific to fly fishing than the Campfire. Find some means of getting local information.
No matter what, I strongly recommend getting a casting lesson from an FFF certified instructor, if possible. I also recommmend purchasing the Lefty Kreh on Fly Casting DVD. Better to not get bad habits, than to try and get rid of them later (&*%$!!!! tailing loops.....)
Scott