Juan Santamaría International Airport, San José: The good-value no-car option is a prebooked shared shuttle direct to La Fortuna: roughly 3½–4½ hours depending on traffic, from about US$30, with departures that commonly include SJO. A private transfer is the sensible upgrade for a family or late arrival. The public-bus budget route means getting into San José first, then the direct La Fortuna bus (about 5½ hours from San José; roughly US$7); it is cheap, not efficient after a flight.
San José, intercity bus connection: Use the direct San José–La Fortuna bus if your schedule aligns: about 5½ hours and around US$7. The alternative via Ciudad Quesada is workable but adds a connection. Treat posted departure times as approximate, arrive early, and allow an hour of slack; this is not a system to build a tight onward connection around.
Arenal/La Fortuna Airport: Domestic flights from San José are available with carriers such as Sansa or Aerobell; the evidence puts fares around US$90 each way, plus a US$7 departure tax. It is a niche convenience, not the default: confirm the operating schedule and arrange the short onward transfer with your accommodation before flying.