I'm flying into SJO and staying at a guest house 3 minutes away in Alajuela. I'm hoping to find what amount I should expect to pay so that I don't get overcharged.
Airport taxis are usually expensive, as is almost anything you buy at an airport.
They are likely to price up a short journey: they won't want to wait an hour for a job just to take a $10 fare.
You could obtain contact details for local taxi operators, and phone them in advance for 'on demand' quotes (not booking in advance). Then when you have gone through immigration call a taxi "right away, I am waiting".
They won't want to take a booking in advance for such a short journey, with the unreliability of landing and immigration times.
Another way would be to use Uber, which operates in Costa Rica. But again, don't make a booking in advance. If you can, ask the airport taxis first, and if you don't like their price, call Uber, right in front of them.