Appropriate zimros for after Shabbat candlelighting (at home)?

Grew up singing Esa Einai and Yedid Nefesh after candlelighting, and then Adon Olam – Yigdal – Vshamru before Kiddush & meal, and finally Dror Yikra – Od avinu chai – Oseh Shalom after birkat. Wondering why my family did it this way — we don’t seem to know. Also wondering, would it be acceptable to add bits from shacharis, like Vhaer eineinu?