In most freestone streams you can get by with just a few basic flies.
1. 5 or 6 mayfly imitations=BWO, Quill Gordons, March Browns, Hendricksons, Light Cahills, and Isonychia will about cover the common hatches. Maybe if you get lucky you will see a few Green Drakes.
2. 4 or 5 attractor patterns. Humpies, White and Royal Wulffs, Stimis, parachute Adams, San Juan worms, and a few neversink caddis.
3. A few black and golden stone fly nymph imitations
4. A green and tan caddis pupa, they are one or the other 99% of the time
5. couple of wet fly patterns like a PT, BWO, and some generic light and dark colored patterns.
6. Few general nymph patterns. Pts. Hare's Ear, and Fox Squirrel will go a long way in a couple different sizes. Maybe throw in a Tellico and a copper john or two.
7 Terrestrials, maybe the most important of all and maybe the most productive fish catchers of the bunch. Ants, Beetles. inch worms. grasshoppers, and bees or wasp.
You would do well to read Byron's or Daniel's fishing reports everyday. They give good advice on not only flies to use but some basic tactics you need to be successful. Pay attention to what people are using that are catching fish. Fish with good fishermen, pick their brains when you can, and observe them when you can. It really is true that 10% of the fishermen are catching 90% of the fish.
All these will fit in one large box or a couple small ones. If I can't catch em with that assortment, I'll be back at the truck drinking beer and eating fried chicken.