Line 1: Post-Eric Staal, Jordan Staal and Victor Rask will have to duke it out in training camp for 1C. Given that I think Jeff Skinner and Elias Lindholm are the two best options at each wing, and Rask and Lindholm drove offense well when they played together, I'm penciling Rask in at 1C.
Line 2: Jordan Staal looked very good possession-wise with Joakim Nordström and Andrej Nestrašil (over substantial playing time) last year, so they'll be a good second line.
Line 3: Lee Stempniak seems to be fairly underrated as a winger (judging from the sheer number of teams he's played for in the last decade), but he'll be a good mentor to finally help Teuvo Teräväinen get off the ground and establish himself as an NHLer. He'll be good for Phillip Di Giuseppe's development, as well.
Line 4 + Extras: Bryan Bickell, Jay McClement, and Viktor Stålberg seem like pretty good 4th liners. Stålberg can even move up a line or two if he needs to. Brendan Woods and Derek Ryan are fine extra forwards.
I think Sebastian Aho will be hard-pressed to find a permanent spot on the roster, unless he blows the competition away in training camp. It might be good for him to start the season in the AHL to get used to the North American rink size and pace of play, and he'll be the first call-up if someone gets injured. Alternatively, if he does amazingly in training camp, he might get 3LW and bump Di Giuseppe down to the 4th line (Woods would be demoted to maintain roster size).
Defense
Pair 1: Justin Faulk is the clear #1 on the right, and he looked pretty good possession-wise in a limited amount of time together with Jaccob Slavin. Plus, it'll aid Slavin's development to play with Faulk.
Pair 2: Pretty much the same as the 1st pairing, except with Ron Hainsey and Brett Pesce.
Pair 3 + Extras: Noah Hanifin is only 19, so getting sheltered minutes with Ryan Murphy is probably a good idea for him. The Hurricanes shouldn't rush him into large amounts of ice time. Matt Tennyson's a fine 7th defenseman.
Haydn Fleury and Roland McKeown, like Aho, will probably start the season in the AHL to transition from major-junior hockey to the big leagues. They'll clearly be the first two called up in case of injury, and Fleury will probably take Hainsey's spot once his contract is up and if he's not re-signed.
Special teams mostly based off of ice time. I originally had Faulk/Hanifin on PP1 and Murphy on PP2, but I didn't think Murphy could handle quarterbacking PP2 by himself, so I moved Hanifin to PP2 and Stempniak up to PP1.