I'll take a stab at this for you. I have been fly fishing for around 40 years so might have an idea or two that'll help.I live in Alberta so being a mentor could be a challenge for me lol

I assume that being in Wyoming you will be looking at trout.
I have found that a good all around rod is an 6wt 8-9 feet long.
Next add a reel with a decent drag system that will hold 100 yards of backing plus your fly line. A weight forward line would be my choice. There are a number of top notch companies which sell starter sets, Orvis, Scientific Anglers, Redington all come to mind.
A fly shop would be the place to pick this stuff up as the staff should be knowlegable. If you have a local fly club that would be a great place to hang out as well. Lots of clubs host begineer classes.
Generally speaking flies are broken down into these classes:
Dry flies are designed to float, generally they imitate adult insects that have hatched.
Wet flies are fished under the surface and imitate immature or hatching insects. Can also imitate adults that are egg laying or have drowned.
Nymphs are immature insects.
Streamers imitate minnows or fry.
Be careful you don't get talked into buying stuff you don't need, you can end up with a wack of gadgets, but then again I have have a wack of gadgets so.....Welcome to a lifelong addiction.
Hope some of this helps. It is a fun way to fish.

Last edited by troutfly; 11/07/12.