The most cost-effective method would be by public bus. It stops by the airport on the way to Jaco. It costs less than $3, but I wouldn't recommend this method. I don't know if anybody knows exactly where that bus stop is, what time it stops there, or how you would know to hail it as it's passing through. So we'll go to the second cheapest option.
Your second best choice would be INTERBUS, like Zebra suggested. They can't do pick-ups at the airport for Jaco, only San Jose. So you would need to meet them at one of their pick-up points. The closest pick-up point to Jaco is the Hampton Suites just outside the airport in Alajuela. Interbus calls that stop
San Jose Rio Grande (Alajuela). So you would need to book Interbus (San Jose Rio Grande to Jaco Jaco) at least 4-5 days before your trip just to be safe. Yes, you want to book Jaco Jaco, because there are 2 other points in Jaco that they drop off at. Once you arrived in CR,you would take a taxi from the airport to Hampton Suites. It should be only a couple of dollars.
The bad part is that there are only 2 buses daily to Jaco from San Jose, they stop for pick-ups at the Hampton Suites at 8:45am and 3pm. It's 2.5-3 hours with the rest stop it makes. The cost of IB is $25/person each way.
You can book them here:
www.interbusonline.com