Each new place we "settle" into introduces completely different "right ways" to get to and from the airport.
The easiest (for the flyer, that is), and usually first, way most of us get there is to catch a ride with friends or family. The added advantage is that you get to extend your visit by that much more. The disadvantage is, well, face it - it's an inconvenience for the driving party.
When I was new to Los Angeles, I had no clue - I thought everyone used cabs! My first trip (yes, I still remember this, 27 years later) was less than 5 miles, cost me $28, and was a comedy of errors; the shuttle would have cost me only $5 (had I only known).
While we lived in the San Francisco Bay Area, we caught on to the rental car method. This ran us roughly the same amount as a shuttle, but had several advantages: we could leave when it suited us, instead of perhaps as much as an hour earlier; it was an unshared, comfortable ride; and I could drop off Rick and all the luggage, turn in the car, and get dropped at the terminal in turn. The only drawback was picking up the car the day before.
In Costa Rica, we tried many different things. Organized tours will pick you up as part of their package, but once you live there, you're not likely to do this. Taxis are reasonable, and if you have more than one suitcase, this is the way to go. But, if you're not moving all your worldly possessions around with you, then the bus is definitely the best option! All you have to do is walk less than a block, make sure you have the right bus, stow your suitcase underneath, pay about $1 each (of course, you need to have colones), and ride it to the terminus. A taxi from there is easy! When friends came to visit, one or both of us would meet them at the airport the same way.
Here in Albuquerque, there is a free bus from Downtown to the airport! For us, this is a 10 minute walk, followed by a non-stop express. Normally, we would do this, but I think we have first-timers anxiety :-). Instead, we're taking the shuttle, at $30 round-trip for 2. At some point, we may look into the car rental method, but I suspect that the bus will win out!
ABQ Sunport sculpture: