A careful installer starts with a room-by-room heat loss calculation, then walks the outside of the house for an outdoor unit spot clear of roof runoff, drifting snow, and, near the shore, high water. About two thirds of Hingham's housing units are single-family detached houses, so yard space is usually available; routing line sets through older walls is often the harder question.
Expect an electrical permit, a light plant authorization number for any service work, and a wiring inspection, handled through the Building Department at Town Hall on Central Street. Wiring inspections are scheduled by phone on Monday through Thursday mornings, so ask the installer to book it rather than leaving it to you.
If the plan retires oil completely, the old tank has to go. Hingham Fire Prevention issues the permits for underground tank removal, so ask who files it and how the tank will be cleaned and hauled away.