All the standard credit cards are accepted in Costa Rica. The most popular ones here are master card and visa, American Express is also supported by some establishments. You should have no problems paying with your credit card almost anywhere.
If you want to obtain a credit card, most local banks will issue them. Credomatic is the local largest credit card company, should you want to contact them directly for a credit card.
Before you leave home, be sure to notify your bank that you will be traveling outside your country, so that their security department does not become suspicious if they start seeing transactions outside the country all of a sudden. Just in case, check that your credit card does not have any restrictions on being used outside the country. Ask about applicable commissions on foreign transactions as well as what the policy is for the exchange rate that they use to charge you in the end.
Why should you find out all these small details from your bank? Mainly because knowing them can save you money in the end. For example, if your bank offers a more favorable exchange rate than the one you get in banks in Costa Rica, you're probably better off charging everything you can to your credit card and paying it off back home. If the exchange rate is not so favorable, you might be better off paying in cash locally.
Always carry some form of ID if you're thinking about paying with a credit card. Before, ID was not required for credit card payments by most places, however in recent years it's become almost mandatory to request valid ID along with your credit card before making transactions.
There is no lower limit for the amount of a credit card transaction, at least no lower limit set by the banks and credit card companies. In theory, you could pay for a pack of gum with your credit card if you wanted to, and the store cannot refuse you.
Always carry the number for customer service of your credit card company in a safe place (outside your wallet and purse!).
ATM machines are available all over the country, the three major networks are BAC, ATH and BNCR. Most ATMs will take a card from any company without complaining, though they might apply a comission if your card does not belong to their network.