I typically fish dry droppers most on small streams, when the water is cold and/or when the stream is predominantly populated with Brown Trout. Brown Trout tend to feed less on the surface than Brook Trout most of the time, and having the dropper can make a huge difference. For Brook Trout, other than in Winter, there’s no need for a dropper, it just gets in the way.
The most common flies I use to suspend a dropper are EHC’s, Stimulators, or Wulffs and Humpy’s, all size 12. This is probably one size bigger than I’d typically fish if just using the same dry pattern alone. This gives you a little extra buoyancy to work with and when picking a specific fly from my box I deliberately pick the one that looks the bushiest with the most hackle. I tend to use the Wulff and Humpy more in the late Spring and early Summer when mayflies are more abundant, and the EHC or the Stimulator from mid-Summer through Fall. With this set up I typically use a pretty small BH nymph…size 16 or 18 BWO nymph or Bird of Prey pattern. Yeah, you sink the dry sometimes, but that’s part of it. I’ve caught a couple of my bigger small streams Browns on sunken dries actually.
All that said, nothing beats a foam Hopper for this technique in terms of suspending the nymph without sinking the dry. With a foam Hopper in size 10 or 12 you can pretty much tie anything you want off it and be fine. I’ve tied big, heavy Stoneflies off a Hopper before, in higher water. Hoppers can be effective dry flies on their own at times, and they’re fun to fish, so I do do it on occasion, but the other patterns above will catch more fish on top in most situations IMO.