Most of the rising fish I fish to are taking mayfly. I occasionally run into sedge hatches, but this rare. So I carry plenty of mayfly flies, both dries and emergers.
My favourite mayfly pattern is a variant of the Parachute Adams. It is a simple to tie fly, the Parachute Improved Kruse #14. I changed from fishing an Improved Kruse to a Parachute Improved Kruse when I saw James Mabin catching a heap of fish on a parachute some years back. I don’t tie an Adams because they take too long with the dubbing and the two colours of hackle.
My emerger pattern is a simple size 16 Hare & Copper with four wraps of 0.20 lead wire. This gets the fly under the surface every time without sinkant, and I probably catch 70% or more of my fish on the emerger rather than the dry.
The key to fishing the emerger and dry together is getting the distance between the two flies right. It should be between 20 and 25 cm. This keeps the emerger near the surface where the fish are because the stiffness of the line keeps the emerger near the surface. Go much longer than 25cm and the emerger starts sinking too far as the leader starts drooping.
You may wish to fish other patterns, or fish without an emerger. I don’t think the flies matter too much as long as they are the right size, and presented accurately. I use the flies I have named here because they are very easy to tie and don’t get beaten up. When I started out fishing the rise I used a pheasant tail as my emerger, and it seemed to be hit quicker than a hare and copper, but it would only last a couple of fish before being wrecked and needing replacing. The time I took tying on a new pheasant tail was a lot longer than the time it took to get a perfect presentation with a hare and copper to get a fish to take, so I culled the pheasant tail out of my fly box.
After many years of fishing without using pheasant tails I decided to give them another crack, and fish them barbless. Previously I had been using barbed #16s, and these got damaged because I needed to use forceps to remove them from the fish. Barbless they survive much better so I use them again, mainly when I have fished a pool on a few evenings and the fish are a bit suspicious of my Hare & Copper emerger.