Ground state properties of a polaron in II-VI quantum wells are investigated by considering both the confined and interface phonon modes which exist in such structures. The Landau-Pekar approach is employed to treat the electron-phonon interaction because these materials are generally much more ionic than III-V compounds. The binding energy and effective mass are calculated by means of a variational method as functions of the well width, and the three-dimensional limits in both the well and barrier materials are examined. Contributions from different phonon modes are studied separately and our results demonstrate the importance of symmetric interface modes in wells of widths ~ 100 Å or less.