An engagement is supposed (at least traditionally) to be a planning period between where the couple decides to get married and when the actual wedding happens, so that the wedding can be planned. Some people don’t use it like that, but traditionally that’s what it is.
Probably depends on how big the families are. The fewer the people, the easier it is to just do the city hall thing. My parents just did the city hall marriage and had dinner with my mom’s dad and brother. Though if all the parents are living I’d have to imagine that the wedding route is normal.