The 'גמ in שבת on :קיט tells us that two angels accompany us home from shul on ליל שבת. To greet them, we therefore sing the שלום עליכם hymn. While, strictly speaking, שלום עליכם is not directly related to the ritual of the שבת table (but rather only serves as a greeting for the angels who accompany someone home to inspect if their home is adequately prepared for שבת), nonetheless, the שבת table provides a set framework within which שלום עליכם can be sung in a sensible context.
שלום עליכם 1 - an Orientalized rendition (!) by NS of Israel Goldfarb's composition
שלום עליכם 2 - the same by FS
שלום עליכם 3 - Orientalized version by FS of Shmuel Brazil's composition
שלום עליכם 4 [LKA]