I'm a dry & dropper junkie - it's how I start out fishing most of the time, and usually what I end up sticking with. For starters - for my dry fly, I like to use something that floats really well, and add just a touch of additional floatant. Humpies, elk/deer hair caddis patterns, stimulators, sofa pillows, heavy hackled parachute flies, or flies with polypropylene wings are good. Then I go with a dropper at least 1 size smaller, two if I'm going with a bead head dropper fly - and I down size my tippet at least one size smaller. The thinner the dropper tippet, the less resistance it creates in the water, and the easier your nymph/wet will sink. Even 6 and 7x tippet can be hard to break - just wait till you snag a tree with that dropper fly...
In general, I tend to shy away from heavily weighted flies (or weighted flies in general) for my droppers. You can add some fly sink (the opposite of floatant) to help get the flies down if you need, or just spit in your hand and press the spit into the fly body so that it's already wet when it hits the water (this will let it sink faster, instead of sitting in the surface film until it soaks enough water up to sink)
I general use shorter casts than most, and watch the currents. Either cast as close to directly up stream as practical, or keep as much line off the water as you possibly can, to minimize how the surface currents play with your setup. Ideally, your dropper will hang almost straight down from your dry fly, but keep in mind that the current on the surface is not necessarily moving at the same speed as it is on the bottom, even through the same slot.
Also, how you attach the dropper plays a role. There's 3 basic ways to do it. Short droppers off your leader, tying the dropper to the bend of the hook of the dry fly, or tying the dropper to the eye of the dry fly.
For years and years I used the in-line method of tying to the hook bend - but I've changed up my game, and have been going eye-to-eye with my dropper flies. I think this gives a little bit better presentation. Some guys believe this also helps with not missing hook ups on the dry fly (some claim that tying to the hook bend prevents hooking fish with the dry - I've never noticed that problem). Whatever way you have confidence in, is how you should fish. Confidence is very important.
I will note - especially when fishing for panfish - dry & dropper (or popper & dropper) works GREAT, and the potential for double hook ups is neat. Happens quite a bit when fishing for schooling panfish, since they're so aggressive.
And think of it this way - you could be indicator nymphing with some gaudy colored hookless strike indicator, and only possibly catch fish with your nymph - or you can fish a highly visible, high floating dry fly as your strike indicator, and quite possibly get some nice dry fly catching going. Double your chances, double your fun.
And once you've gotten comfortable fishing 2 flies, you'll feel that urge to try 3 flies, which really isn't any more difficult than 2, except when it comes to deciding which flies to chose (a big dry fly like a grass hopper works great for this as the top fly, and I usually go with a natural, tame colored nymph and a wildly colored attractor wet fly - let the fish choose what they want to eat). You might also dabble in working "casts" of wet flies, swinging 3 wets through a run. That can be a hoot.