I use a floating line - generally a double taper, but a weight forward is OK. You wouldn't be casting far in any high stick nymphing so I don't think taper matters all that much. I go with DT because I think it roll casts better and that is what I have used for a long time and is a habit. I like the floating line with a slack leader because I can switch quickly to a dry or dry dropper if the fish move up.
My favorite set-up is a Greys Streamflex 10' 3 wt with a 4 wt floating DT line and a 10' leader. I can switch to dry flies pretty quickly. This works for 90% of the places I fish, but the problem is I really can't crank long casts out so if I have to switch to dries on larger water like the Delaware I can't reach some fish. Medium streams I can fish fine. At the Delaware I like a 9 1/2' 5wt Z-Axis with a WF line which has a decent length for nymphing but can reach a whole lot more fish with dries. Your style has a lot to do with outfit selection, but I generally go for softer, lighter rods unless distance makes me go to a heavier, faster set-up.