Notes
The limes you will normally find in the United States are Persian limes. These are green and are about 2 to 3 inches across. This is great for making drinks.
Farther south, you will find Mexican or Key limes. These are much small than Persian limes--on 1.5 inches across at most. They tend to have a thinner skin than the Persian lime, and the juice is a bit tarter. They work well in drinks.
Another lime, called a Kaffir lime, is not that good to use in drinks. Though the leaves of a Kaffir lime tree are fantastic for use in Thai, Lao, and Cambodian cooking, the lime itself is somewhat lacking. Stick to Persian or Mexican limes.
If you need to substitute lime juice for lemon juice, keep in mind that lemon juice overall is tarter than lime juice. Adjust your sweetener accordingly.