Most Costa Ricans do not own cars so public transportation is very good throughout the majority of the country. Costa Rica's two international airports are located in Alajuela and Liberia which are the main hubs for public transport. From San Jose or Liberia you can hop on a public bus, hire a private transfer, rent a car, or fly to one of the many regional airports.
If you are looking for freedom and don't want to be on someone else's schedule, a rental car may be the best option for you. If you are going to travel to the far reaches of the country you will probably need a 4wd vehicle but it is not always necessary as the roads have been improved over the last few years. Ask the rental company what car they would suggest to make sure you can arrive at your destination. I also recommend renting a GPS. There is a lack of road signage in Costa Rica and more often than not you will get directions using landmarks such as trees, fence lines or even cows. This always leaves your second guessing where you are and it is never a good feeling to be lost. Paying just a few bucks a day for a GPS can save you hours of frustration. Also note that some credit card companies offer some form of rental car insurance. Check with them before you get to Costa Rica to see what options they have available and if it could save you some money.
The Costa Rica bus system is very good, inexpensive and is what the majority of the country local population uses to get around town and around the country. Some remote towns may only have one or two buses serving it each day while larger cites have buses leaving every hour from early morning through late evening going to every corner of Costa Rica. The cost to travel by bus is affordable and they normally run on a tight schedule.
Local Buses are a great way to get around the larger cities with pickups around every 20 minutes from each bus stop. They serve Alajuela, Cartago, Heredia, and other suburbs of San Jose. The buses can be a crowded with standing room only but most cost less than a dollar. To make sure the bus stops, reach your hand out around waist level and shake it when you see it coming. This also works to with taxis.
Private Transers are a great idea if you don't want to drive but still want the freedom to be on your own schedule. Most companies have very nice vans so you can stretch out and enjoy the views without worrying about getting lost. The drivers have traveled the roads many times and can suggest great places to eat and offer some insight into the town you are traveling to. You can hire drivers for the day or for your entire trip. Prices are very reasonable.
Regional Flights and Charters are another way to get around efficiently, especially if you are traveling to hard to reach and out of the way places. Costa Rica is very small so most regional flights are less than 45 minutes and cost less than $100. Nature Air and Sansa both have well maintained planes and boast great safety records. Most airlines charge extra for oversized and over weight baggage, check with the airlines to confirm space before your scheduled flight.