The weird thing is, as trout are far less diverse in their habitats and diet than carp, it's arguably more possible to have a generic box of trout flies that will travel successfully to most locations than it is for carp, which is partly why I find the question about carp flies so odd. I keep thinking about it, maybe it's because I do so much carp fishing on very different waters. The thing is, carp can eat just about anything, but it doesn't mean they will. They eat, (mostly) what they're used to, which is why what constitutes a good carp fly varies greatly depending on the water it'll be used in. Of course there is some overlap but it's definitely better to tailor your box(es) to the water you'll be fishing. For my fishing there are 3 kinds of waters that I need to consider.
The first are nutrient rich, silty, slow moving rivers and stillwaters. Generally the flies for this kind of water need to be smaller. Little backstabbers, chenille worms, sporks and scruffy buggers or woolly worms are the kind of thing I'd suggest putting in a box for the carp that live in these places.
Then there's the tailwaters. Many of the freestone rivers in this part of Japan are dammed, which obviously changes the forage available to the fish. I'll still carry some worm flies here, but will certainly be moving more towards meat based prey items small (15-20mm) crayfish patterns or small sculpins. I also carry some peeping caddis and larger mayfly nymphs. I know the insects tend to be smaller on tail waters, but for some reason the rough shape seems more important than size in my experience.
The last type are the less nutrient rich rivers and mountain lakes. This is where the biggest shift in size and type of fly happens. Meat is probably the first choice here, Gobies/sculpins, baitfish and bigger crayfish patterns are more likely to work here. 50-70mm seems to be the sweetspot, but I often accidentaly catch carp while targetting smallmouth bass on these rivers using much bigger flies; an 18cm bucktail deciever is probably the biggest yet.
Most patterns in will probably be tied in at least 2 weights, preferably 3. Each box also has a few other patterns, 15-20mm glo-bugs tied on stout carp hooks are a must, some quick sinking attractor patterns with some flash and colour and lastly some mulberry imitations and hoppers in summer. Yes, it's possible to take one box anywhere and you'll probably have something that'll work. But if you're going to be regularly fishing for carp- which you should because it's super fun and challenging- it really is best to build a selection of patterns suited to where you're targeting them. I think from my 3 categories it's easy enough to extrapolate a rough outline of the kind of thing you want and then you can tweak it.