Palm Beach International Airport: This is the airport to use. Jupiter is roughly 20–30 minutes by rental car or rideshare, depending on whether you are headed to the inlet/beach or western Jupiter; budget about $35–55 for a car service/rideshare before surge and tips. A shared shuttle may start around $28, but it is slower and only makes sense for a solo traveler who is not renting a car. There is no direct, useful airport-to-Jupiter rail link.
Fort Lauderdale–Hollywood International Airport: Only choose FLL for a materially cheaper or better nonstop flight. A rental car or rideshare is about 1½–2 hours in ordinary traffic, longer at rush hour. Brightline can take you from Fort Lauderdale to West Palm Beach, but you still need a roughly 30-minute car/rideshare onward to Jupiter; it is viable only if you are deliberately avoiding a rental car.
Miami International Airport: Use MIA only when the flight is decisively better. Driving is typically about 2–2½ hours and South Florida traffic can make that optimistic. Tri-Rail or a Miami-to-West Palm Beach rail journey followed by a rideshare is possible, but it is not a good airport transfer with luggage; expect a multi-transfer trip and well over two hours door to door.