Here's what I think will likely happen (in other words, not exactly my ideal scenario, but a very good one nonetheless, and what I think is more realistic):
1) TRADE: Stepan and Klein for Ryan O'Reilly
2) TRADE: Dorsett for a pick at the draft
3) SIGN: Ryan Carter (900k) and Mark Fayne (1.9)
4) RE-SIGN: Zuccarello (4.0), Stralman (4.0), D. Moore (1.6), J. Moore (1.5), Carcillo (900k), Kreider (2.5 bridge), Brassard (3.75)
(Boyle and Pouliot walk)
Zuccarello (4.0) / O'Reilly (6.25) / Nash (7.8)
Kreider (2.5) / Brassard (3.85) / St. Louis (5.6)
Hagelin (2.250) / Miller (894k) / Kristo (850k)
Carcillo (850k) / Moore (1.6) / Carter (900k)
Fast (805k)
McDonagh (4.7) / Girardi (5.5)
Staal (3.9) / Stralman (4.0)
Moore (1.5) / Fayne (1.9)
Allen (925k)
Lundqvist (8.5)
Talbot (563k)
(assuming the cap is between 70 and 71, which is wishful thinking at this point):
CAP PAYROLL: $69,736,667
CAP SPACE (22-man roster): $1,363,333
That's already including the cap-space of a 13th F and 7th D on the roster.
Zuccarello O'Reilly Nash - Versatile line, should be strong in all 3 zones. Zuccarello is the playmaker. ROR is the gritty, sneaky center who breaks up plays / steals the puck and leads the transition the other way, and Nash is ... well hopefully he's Rick Nash and not the guy who wore #61 for NYR in the playoffs.
Kreider Brassard St. Louis - Speed and skill: Kreider brings the speed, physicality, and energy, while Brassard distributes the puck and St. Louis does what he does best.
Hagelin Miller Kristo - Miller and Kristo get to use their strengths and play their game with minimal pressure by having Hagelin's speed to insulate them, and erase any turnovers or mistakes they make. Substitute Kristo for any of [Kristo, Haggerty, etc]. This is a forward spot to be won during camp.
Carcillo Moore Carter - A very smart fourth line: Carcillo's speed, energy, and agitation with Moore's smarts, solid defensive play, great skating and Carter's big body presence down low and in the corners.
McDonagh Girardi - Nothing needs to be said. Girardi should bounce back to form. He played a ton and was clearly banged up. The guy is never 100% (blocking so many shots and taking so many hits going back to get the puck) and he's usually very solid.
Staal Stralman - Steadiest NYR pairing at times during the playoffs. Can eat up minutes against top players and contribute offensively occasionally.
Moore Fayne - Moore's greatest attribute is his skating and ability to carry the puck through the neutral zone. If he figures out how to finish, or make the next right play to create quality scoring chances instead of just a flashy, speedy rush up the ice that results in a turnover, or weak shot attempt, he'll be a dangerous player to have. Fayne is underrated IMO. He's very steady, has a heavy RH shot, and while not flashy at all, he gets his job done and never seems overwhelmed.