Death in Paradise (2011)

The fictional Caribbean island of Saint Marie supplies the sunshine, a run of fish-out-of-water British detectives supplies the comedy, and nearly every case ends with the classic gather-the-suspects reveal. Each episode is a tidy, self-contained puzzle, so you can dip in anywhere without homework. Don Gilet's DI Mervin Wilson leads the current era, and with fifteen series behind it, the back catalog is deep enough to last a whole winter. If you only try one show here, make it this one.