After an August that seemed to bring the closing of nearly every Broadway show in quick succession, the New York theater world is gearing up once again for a season that feels simultaneously cautious and offbeat. On Broadway, there are fewer big-gamble musicals than last season, with producers opting for a steady supply of jukebox, from Tina Turner to Alanis Morrissette, but there are also straight play imports from London and summer theater festivals, as well improv rap, just to mix things up. Elsewhere, you’ll find intriguing revivals, directors taking big swings, and of course, many gestating movie-to-musical adaptations.