Keflavík is the international gateway for a southwest trip. Reserve a return at KEF explicitly if you collect elsewhere.
The airport lists some suppliers with service desks inside the terminal, while others use a driver meeting point or shuttle. Its rental map gives company-specific instructions; do not assume all airport offers are terminal walk-ups.
A car can link rural accommodation and sights beyond scheduled public transport, but it also makes you responsible for weather-led decisions. A guided excursion can be a better fit if you do not want to drive in unfamiliar winter conditions.
Compare airport collection with a later collection if you start with a city stay. Include the transport to a different rental branch and any extra parking nights when comparing the total cost.