This is a popular question. The only problem is that the answers are nearly worthless! 🙂 It's not that the responders are misleading or wrong, it's just that everyone has a different style... and more importantly, a different stream!!
I used to fish Clarks and Stony Creeks before my accident. One was great for caddis pupae. It was a goto for me. On the other side of the mountain, the same flies were very sporatic. So you have to know your stream really well. So, watch the hatches, turn over rocks, check out spider webs and the trees to see what is hanging out on the stream.
That said, if you fish a variety of streams, you'll probably find that a short list of flies will be your favorites. I loved dry fly fishing and was real big on attractors and general patterns. Guys who match the hatch or like nymphing may have a different list:
Dries:
Royal Wulff (or if you start tying, royal trude... it's just as good, and much, much easier to tye. Plus it won't twist your leader as much) 16 & 18 is great. Most guys would say 14, but you can fudge sizes DOWN not up, so if you are on a budget, skip the larger flies. In the summer, 12's &14's are good for beetle hatches.
Lime trudes 16 & 18. Great for sulphur hatches. I felt much more confident with a lime trude than a strict imitation.
Adams 16 through 22. In the summer, downwing styles are good for mosquito and black fly hatches, but the traditional is good in early spring. An Adams 12 is OK for the Quill Gordon hatch, but the bigger the bug, the better the imitation should be... also the longer the hatch (in days) the better the imitation. Adams 18, 20's and 22's are good for BWOs and midges. Those are hatches you'll fish often.
The Usual 14 to 18 good caddis and mayfly pattern. A pattern you can color with pens to match any hatch
Tan Elk Hair Caddis 16&18. Guys will scream I am not recommending more colors and sizes. This is what worked for me 90% of the time.
Orange Ant 18- This you might need to get tyed for you. It's worth it. Tye it with bright (hunter's ornage) orange dubbing and white hackle. Do not trim the hackle.
Black ants 12 & 16's down to sizes you can't see any more.
White Cahill 16&18 good for late sulphurs and of course, cahills which can hatch all summer.
Beetles 10-14. Crowe beetles are great, but they get beat up real fast. It's worth it IMHO. BTW you can fish ants and beetles from ice out to the first heavy frost.
Bivisbles 14-18. great for midge hatches (especially if you go smaller) caddis and general searching. Great pattern to put on early and experiment with various presentations.
Wets:
Patridge and Orange 12to18, I like to upsize my wets and nymphs a bit. Good pairing with the bivisible above, it can be fished many different ways
Hare's ear wet 12-18 fish it any time, any hatch
Pheasant tail wet 12-18 any time, any hatch
Nymphs:
Guys like wooleybuggers. I never had the same kind of luck with them. Good luck to you, if you carry them
Stonefly nymphs. 8(black) or 14(brown) or 18(black). There are a large variety of stoneflies. They take two years to mature, so you can carry many more sizes than that, and more colors. That's what I like. For some reason, all white and all golden brown do well in 8's too.
zug bugs 14. This fly could be anything. That's why you need it.
Pheasant tail 10-16. You could carry this down to 22 or as big as 4s but I showed some restraint and limited the size range to meat of the line up. Carry them unweighted to start, as your fly collection grows, add beadheads and weighted beadheads to fish faster and deeper.
Hare's Ears 10-16 as with PT's. This is another could be anything fly
Streamers:
Shenk's White Minnow-8-14 When everyone else is catching fish on buggers, this is what I used. In fact, it's good in a hatch. 'cause when a hatch brings fish out to feed, the big fish are feeding on the little fish.
Muddler Minnows. 8-14 Unweighted and greased, they can be a cricket or a big caddis. Weighted, they are a really good streamer. Fish them tight to the bottom.
That's plenty to get you started!
