You live near some great water for both trout and bass---- and some monster trout in some of those like the White. And it's great that you have an uncle that can help with the casting and getting you off to a food start.
As far as your questions.... the casting mechanics for bass and trout, and all fly fishing for that matter is basically the same. In addition to casting, you'll want to learn how to present a fly so it drifts naturally with the current to control "drag". This happens when your fly line is in slow current and your fly line is in faster current, like when casting across a stream. In no time the faster current pulls the fly line downstream, and you'll see your fly waterskiing after it. Generally this is more important in trout fishing-- bass and other warmwater fish tend to be more forgiving, but you'll want to learn it for them too if you fish in streams. The process of controlling drag is called "mending". Here's a link:
Fly Fishing, Fly Presentation, Mending - MidCurrent
After you get the basic mechanics of the cast down, you'll want to learn some techniques to help get longer drifts like reach casts, pile casts and s or wiggle casts, but for now concentrate on the basics.
As for flies, there are local favorites, but here are some good ones that work anywhere. If you asked 10 different people you'd probably get 10 different lists, but here goes:
Good flies for bass AND trout:
black woolly bugger #8 weighted or bead head for fishing deeper water, let it sink a bit and strip back to you.
black marabou muddler #6 get a weighted one, fish the same way as above, great for big bass and big trout.
Grasshopper pattern size 10- for the surface, a good summertime pattern panfish will whack it too.
White Wulff size 12- another dry fly, panfish will whack it. This is not normally a fly I'd include on a must have list, but this is especially good for bass and trout if you get a hatch of large white flies in summer. They hatch in the evenings in August throughout the E, SE and MW on slower streams/rivers with muddy bottoms and the fishing can be fantastic bringing up every fish in the river if you get a White Fly hatch on your streams and you probably do on at least some of them down there.
For bass add:
a big popper with rubber legs, size 6 especially good for ponds with lily pads, or along slower stretches of streams
in late evenings.
Clouser Minnow #4 in chartreuse, and if you fish in rocky streams for SMB, get one that's brown over orange to imitate crayfish too.
For trout add:
Parachute Adams 14 and 16 (slow water dry)
Elk Hair Caddis tan size 14 and 16 (slow and fast water dry)
Stimulator size 12 Orange, yellow or green (fast water dry and good to skate across slow water for smallies)
Partridge and Orange Soft Hackle size 14- a wet fly to swing in the current
Bead Head Pheasant Tail Nymph size 16
Bead Head Gold Ribbed Hares Ear size 14
For panfish they'll also hit all the trout flies listed above but these are a lot of fun in ponds and slow water:
panfish poppers size 10 or 12
Foam spiders with rubber legs 10 or 12
You'll want to get some dry fly floatant- either liquid or paste type to put on dry flies about $3-4.
You'll also need some tippet spools- thin mono to tie onto the end of your leader. (As you clip off flies you'll be shortening your leader). Just tie on about 2' or so to the end of your leader with a blood knot. Since leaders are tapered to allow the fly to turn over and lay out properly at the end of the cast, you'll want tippet of different sizes, depending on the hook size of the fly you're using. heavier tippet for bigger flies, lighter tippet for smaller flies. To figure out the tippet to use, divide hook size by 3 to get the size X tippet. As an example, a size 12 fly divided by 3 = 4x tippet.
You'd want to get something like this, notice that there is some overlap, you don't have to go too crazy:
2x for bass poppers, #6 muddler, and clousers and buggers
3x for bugger, hoppers, panfish popper and foam spider
4x for foam spider, 12-14 dries, wets, nymphs
5x for 14-16 dries and small wets and nymphs 14-16
Hope this helps.