Raise the underlying limits first
Most households get more protection per dollar by moving auto liability up from the state minimum than by adding a layer on top of a thin one. An umbrella also requires qualifying underlying limits, so that step is usually necessary anyway. Done in the right order it sometimes turns out to be enough on its own.
The question is what a judgment could reach
Equity in a home, savings outside protected accounts, and future earnings. A household renting, with modest savings and no unusual activities, has a weaker case for an umbrella than one with a paid-off house or a swimming pool. Neither answer is wrong; they are different situations.
Certain activities change the answer on their own
A pool, a dog with any history, a rental property, a teenage driver, a boat, hosting frequently. Any one of those raises the ceiling on a claim enough to justify a layer regardless of net worth, because the exposure is not about what you own.