I've just started using RIO's European Nymphing Line (Cortland also makes a dedicated line, in 160gr and 140gr weights) with my Hardy Zenith 10' 3wt. The line is mostly a response to recent competition rule changes on leader length, but it also has some significant advantages compared with a traditional fly line...
It's very thin diameter and very lightweight... this improves your ability to hold the line off the water at a distance (avoiding line sag/belly) from line weight and wind which improves your capability for a drag free drift. In comparison to very long monofilament leaders it has very little memory and is easy to see. Also, unlike a conventional fly line, it doesn't tend to fall down (backwards) through the guides (which is a pain in the ***, and happens more frequently because you are holding the rod high when nymphing)
You can also use a substantially shorter leader with these lines than you would with a typical euro nymphing setup. I'm currently using 3' 20lb Maxima Chameleon, 2' 15lb, 1' 10lb, and 1' of 8# hi vis, with a short section of 6# terminating in a tippet ring. This is based on what I've picked up... I need more time to decide if it's right, or even necessary. I'm pretty sure performance would be perfectly acceptable with short section of level mono + tippet. The tip of the RIO line is hi-vis and can serve as all the indicator you need.
The nymphing lines have just enough weight to toss a dry/dry-dropper setup at the distances you would typically fish in competition (less than 40'). My limited experience is with the Rio variety, but from what I've read, the Cortland line in 160gr might be a better choice for your particular rod, as the CZN 4wt is a bit stiffer action.
I have two reels (The Okuma SLV 4/5 is hard to beat for $42). I used the 4/5 to help balance the rod, and for a bit faster retrieve. Because the nymphing line is such small diameter, I was able to put an entire 100yd spool of 30# backing on and could probably stand to put at least another 50yds on. My second reel is spooled with a conventional fly line in 3wt, double taper. That's what I use when I plan to do predominately dry fishing, or fishing beyond 40'.
Casting is more of a lob/fling. You use the soft flexible tip to do the work, and the trick is just getting it loaded up. It doesn't take long to figure it out enough to be effective. It might take a while to make it look pretty.