Fly selection is trumped by stealth and the right fish 10 out of 10 times. Yes the right fly helps, but finding an actively feeding (aka not loafing or cruising fish, think face in the mud, tail up) drastically increases odds of a take.
That said, my go to patterns are anything with bead chain eyes that rides hook up and gives the general representation of a juvie crayfish, insect larva, leech, etc. Think bonefish flies with more rubber legs and marabou.
Lastly, big carp put every trout that swims to shame when it comes to the fight. I've been fly fishing since I was 9 and I'm dangerously close to giving up trout all together. Carp are everywhere. Carp get large. And carp pull like a 3/4 ton truck. Anything above a 6 weight will work, but my rig of choice is an 8 weight with a saltwater reel and a spool of general purpose trout line in the matching weight. Distance is not a factor. Stealth is the key. When you're not slinging arrows or stinky bait, carp get real spooky. And will alert all their buds that something is up, shutting down the bite for a good stretch of water. A flouro leader in 3x will handle most ND fish well. And don't forget the cottonwood hatch! Catching a 15lb golden ghost on a white dry fly is pretty intense
