Hey Woodrow, welcome to the board, glad you joined us.
I think that'll be a GREAT set up for what you'll be doing.
Lefty Kreh is one of the masters, so you can't go wrong with his DVD. You might also want to google "Tight Lines Fly Casting You Tube" for a 3 part vid series that's a pretty good intro to the basics. There's also a site called "sexyloops" that has a lot of fly tying videos online. They're all free. The only caution I'd give is even though Sexyloops - the best fly fishing and fly casting instruction seven days a week
is a fly fishing site, because of the name, I wouldn't search for it at work.... you're liable to get the whole HR dept stampeding your way...
In addition to learning a "regular" fly cast, with a back cast, you'll also want to learn how to roll cast, and some "specialty" casts like the "bow and arrow cast" that will allow you to get the fly on the water in tight quarters, without leaving flies in trees--- though they'll be some of that too.
If you're going to be fishing small mountain streams, I'd keep the leader on the short side, say 7 1/2 feet tapered down to 3X and add about 2' of tippet. Tippet size could vary a bit from heavier 3X for larger weighted flies, to 4X for most other flies and 5x for some of the smaller stuff.
Fish in those streams are generally not too picky, and since the current is typically pretty fast, they tend to whack stuff as it zooms by, and you can get away with larger, heavily hackled flies that are designed to float well, and you don't have a lot of fish coming up with magnifying glasses to inspect everything.
Some good flies to have would be some dries, nymphs, and some larger heavily weighted flies to cover the water column from top to bottom. Early season, a lot of the action will be subsurface, but as things warm up, you'll have a blast on top.
Royal Wulff and/or Humpy size 12 and 14
Tan Elk Hair Caddis 14, 16
Stimulator, green, yellow or orange size 10 or 12
Parachute Adams 14, 16, 18 for slower water stretches and pools
Bead Head Pheasant Tail Nymph 16, 18
Bead Head Gold Ribbed Hares Ear 12, 14
Bead Head Prince Nymph or weighted stonefly nymph size 10
Bead Head Woolly Bugger in black and olive size 8 or 10
As it heads towards warmer weather, stuff like beetles, ants and grasshoppers would be great to add in summer.
I'm sure you'll run into some real jewels in those mountains. Lots of beautiful, wild brook trout, small but scrappy. You'll have a blast.
On some of the bigger, slower water lower down you might want to add some smaller flies like Parachute Blue Wing Olive dries 18 and 20, and some smaller nymphs like zebra midges 18 and 20 to use as droppers off some of the dries, and to look to hatch charts or local shops for specific advise to match hatches on specific water, but these flies should work there too, especially in faster runs and bumpy water sections like riffles etc.
Good luck, and again welcome to the board. Looking forward to hearing about your adventures.