I probably know more about Football than I know about basketball. Like you said, I know a few basic things about coaching in basketball, but I'm certainly not an expert by any means.
I'd say Phil Jackson is probably the best suited out of the guys you mentioned, because his Laker rosters in 2008 and 2009 were somewhat quite similar to the roster we have in New York right now. Several star players, a weak defender at the starting PF spot (Gasol <-> Amar'e), a tall and physical center (Bynum <-> Chandler), a strong bench with several impact players on it (Ariza, Farmar, Brown, Odom, Walton <-> Smith, Novak, Jeffries, Davis, Fields/Shumpert). And he's played in New York and doesn't have to prove anything to anybody (Won't let the pressure get to him or his players).
So in theory he should be the best coach for our current roster. If he can't lead this wildly assembled roster to victory - probably nobody can.
Jerry Sloan: Great coach, bt relies on the PF-PG pick and roll very much. Which role would Melo play in his system and can he deal with a weak interior defender like STAT? Also unproven in a big market, Salt Lake City is a different cup of tea.
Hubie Brown: Probably too old and too much of a father or grandfather-figure. He'll give the players great advice and try to get the best out of them, but the situation might be too much for him to handle at well over 70 years old.
JVG: Dolan won't ever sign him again. He'd be the second best candidate after Jackson imo. Only negative on his CV is the fact that he was a one-and-out. The 99 Finals were followed by 2 frustrating playoff exits afterwards, despite a good roster.
Pitino: I'd give him a month before he'd be gone. Massive clash of egos with Melo and probably STAT. Too emotional for the NY spotlight. Been here - didn't work.