Palm Beach International Airport: This is the airport to use: it is roughly 10–15 minutes by taxi/rideshare from downtown, usually a far better arrival than Miami or Fort Lauderdale. For the budget option, Palm Tran Route 44 links the airport and West Palm Beach Intermodal/rail station; allow about 25–35 minutes including the walk and wait, with a local-bus fare around $2. Do not pre-book a $15-plus shared shuttle for this short urban ride unless you need door-to-door help.
Miami International Airport: Use Tri-Rail from the Miami Airport Station to West Palm Beach for the cheap, practical option; allow roughly 2 hours station-to-station plus airport transfer time, with fares around $5. Brightline is faster only if you are willing to take Metrorail or a taxi from MIA to MiamiCentral first, then pay the higher intercity fare; it is not an airport train.
Fort Lauderdale–Hollywood International Airport: It can work, but it is not a clever substitute for PBI. Take the airport shuttle/ride to the nearby Tri-Rail station, then Tri-Rail north to West Palm Beach; count on about 1½–2 hours door to door and a low single-digit rail fare plus the airport connection. A direct rideshare is faster but can become expensive in traffic.
West Palm Beach rail stations: Brightline arrives at its downtown station by Evernia Street, useful for Miami, Fort Lauderdale, Boca Raton and Orlando. Amtrak, Tri-Rail, Greyhound/FlixBus and Palm Tran use the West Palm Beach intermodal station west of downtown. From either, downtown/Clematis is walkable; Ride West Palm Beach and the on-demand Rose Trolley fill the short last-mile gap. Brightline and Tri-Rail are not interchangeable: Brightline is quicker and more comfortable; Tri-Rail is the inexpensive commuter option.