If the load consists only of essential appliances such as lighting, refrigerator, and router (consuming 1 kWh per day), is a 1kW or 2kW photovoltaic panel more suitable?

Your daily electricity consumption is only 1 kWh. Even considering the approximately 80% charging and discharging efficiency loss of the photovoltaic energy storage system, 
the actual required photovoltaic panel power generation is about 1.25 kWh/day.

The minimum power generation of a 1kW photovoltaic panel (3.5 kWh) is far higher than the demand, which can fully meet the power supply needs, and the excess power can be charged into the battery for backup.

The power generation of a 2kW photovoltaic panel (7 kWh) far exceeds demand. Most of the electricity is either wasted (without energy storage or grid connection) or requires larger capacity batteries for storage, which increases additional costs.