First and foremost the dropshot technique is extremely underrated and on the toughest days can help to win tournaments. Personally I use mostly 4 - 6 inch roboworms, with the occasional 7 if I'm fishing slightly heavier line and looking for bigger fish. Use your imagination and think outside the box, because there are a number of different plastics you can dropshot with. You can nose hook baits when you fish areas without a lot of timber or cover, but usually i'm texas rigging my worm on a trokar light wire finesse hook.
As far as rod/line are concerned I fish a 20 lb main line braid (usually suffix 832) with a 7-8 pound leader most of the time. As for the rod length I like a 6'10" to 7' Medium or Medium Light with a fast or extra fast tip. I've fished a number of rods, but the one I like the most is a Megabass Orochi F3-611XXS. This was a rod designed by Aaron Martens and has everything you will need.
I find the best time to fish dropshots are during the hotter days of the spring and summer, but I find even more success with this when confronted with cloudy skys or overcast conditions when fish are not as tight to cover or structure and are roaming. With that being said i have still had great days during blistering hot sunny days when the fish will not bite anything else. Hope this helps!