Go to the Grizzly Hackle fly shop in Missoula for starters and ask some questions and tell them what your up to. Just remember, fly shops are expensive but are good for information. Ask them about classes and pick up a book. 'Fly Fishing For Dummies' is a good one. Take a look at Bob Wards. They are a good store with good prices and you might get some good info there and find beginner gear. If Gart Sports is still there, they are a good source of less expensive good gear. There is that other sporting goods store there whose name I can't remember that is good for some things too.
For the water in your neighborhood, Bitteroot, Clark Fork, Rock Creek and so on, a 9 foot 5 weight rod will serve you best, IMO. It is the most versatile and is the most popular for a reason. You can likely cast some rods at the fly shop and they can help you with a decision on what kind of a rod you might want to get. As far as getting one rod to fish both trout and salmon, I don't think I can give a suggestion on that. I know of no salmon to be fished in your area except a lake or two in the western part of the state that have kokanee. And they are small enough to be taken with a trout rod. Steelhead not too far away in Idaho.
Cortland lines are a good place to start for price and quality. Reels? Orvis 'Battenkill' and 'Clearwater', Cortland 'Vista Disc' (I just saw one go for 22.00 new on ebay) and 'Pro Cast', Okuma 'Sierra' and others, Allen 'Trout Series', Redington 'Crosswater' and 'Pursuit', After you do some research in the local stores and look at the websites and ebay, you can decide what's best for you and your budget. Don't let anyone talk you into a reel less than 3" in diameter. Preferably 3.25".
For rods? Look at St Croix, Ross Worldwide, Temple Fork Outfitters, Redington, Cortland and some others.
In your beginer/budget class, get the fastest, (stiffest), most expensive rod you can afford. In the less expensive class of rods, the fastest=medium action. You will be glad you did. Rods are no place to cut corners. Look online to get an idea of prices and compare with what you come up with at your local stores. You will most likely buy from them anyway. But it doesn't hurt to get a feel for what the market is like and read the reviews. You can learn alot and shop alot right at home, online.
You may have other places in and around Missoula that I have forgotton or have come in since I left the area. Like you said, it's fly fishing heaven and the stores there cater to the fishing angels. So they should be of the most help to you. Just spend as much as you can afford so you won't outgrow your outfit to soon.