I think any heavy and SLIM flies will work. I love high sticking as well as mixed with European nymphing styles. If you are a big fan of high sticking, you will love it and learn it quickly!
I would say CZ nymphing is very "aggressive" type of nymphing. Unlike wetfly swing, You are somehow "precisely" leading your flies in to a certain spot/zone. I usually pull (lead) my flies into the route I already "designed". At the end of the drift, I would let the flies raise up and might take some followers.(just like regular indicator fishing). I remembered Velvadi mentioned that you want to do some "micro hook set" when you think your flies are drifting by a hot zone.
When said "Lead the flies", I think the important thing is "feel the flies and feel the bottom". I think I like to feel the weight of my system and the feel they bounce along the bottom (every once of awhile). When I feel these two things, I know I have the authority to control my system...speed/depth/direction
The main difference between CZ nymphing and high sticking is "leading the flies". 1) This means I need to "pull" my system slightly faster than the current. 2) Also I need to keep the flies deep and contact with the bottom. That is the reason that heavy and slim flies come into play. If my flies or system too light, I won't be able to "lead" the system. The current will divert my flies all over the place. (Usually I use this CZ nymphing in a relative fast current or pocket waters; I use high sticking in a relatively soft water... cause I don't have confidence to lead the flies right...).
Beside the weighted nymphs, tippet size is the other important factor to me. The fine long tippet will help your system "cut through" the current and give you more authority to lead the flies. Sometime I use 4x or 5x tippet straight. By using fine tippet straight, I also can reduce the flies weight (more natural dangling of the end fly). Also the current will have less impact in disturbing your system.
I am a biologist grew up with a fishing rod in my hands. I have been fortunate enough to embrace my love of art and science in my career. Most of my free time were well spent in the nature, either studying bird behavior or chasing variety of fish with fly rods. My favorite art medium is watercolors, I love the natural and spontaneous feel created by watercolor pigments. I am currently a post-doctoral research fellow at Harvard University. Welcome to my website. Mark